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Advances in Computational Mathematics and Applied Mathematics
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Advances in Computational Mathematics and Applied Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: closed (18 April 2025) | Viewed by 13865

Special Issue Editors

Dr. Tao Liu

E-Mail Website
Guest Editor
College of Sciences, Northeastern University, Shenyang 110819, China
Interests: deep learning; reinforcement learning; multiscale methods (multigrid and wavelet); homotopy method; inverse and Ill-posed problems; parameter reconstruction
Special Issues, Collections and Topics in MDPI journals
Dr. Fazlollah Soleymani

E-Mail Website
Guest Editor
Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran
Interests: computational finance; iterative methods; computational mathematics; stochastic differential equations
Special Issues, Collections and Topics in MDPI journals
Dr. Qiang Ma

E-Mail Website
Guest Editor
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China
Interests: structure-preserving algorithms for differential equations; numerical methods for stochastic differential equation
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Computational mathematics and applied mathematics are two closely related, but each topic has its own emphasis in the field of mathematics. In computational mathematics, most research focuses on numerical analysis and scientific calculation methods, such as interpolation and approximation, numerical methods of differential equations, numerical integration, matrix computation, and linear equation systems. With the development of large-scale computing and parallel computing technology, computational mathematics has shown stronger capabilities in handling large-scale data and complex problems. In applied mathematics, most research focuses on practical applications in various fields, such as physics, engineering, economics, finance, geophysics, computer science, social sciences, biology, and medicine. Applied mathematics has made significant breakthroughs in optimization algorithms, data mining, and machine learning, providing strong support for the development and application of science and technology.

This Special Issue will provide a platform for researchers to share their latest advances in computational mathematics and applied mathematics, as well as their applications in solving real-world problems. We invite researchers to submit original research articles, reviews, and short communications related to the above topics. All submissions will undergo a rigorous peer-review process, and accepted papers will be published in this Special Issue of Mathematics.

Dr. Tao Liu
Dr. Fazlollah Soleymani
Prof. Dr. Qiang Ma
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • partial differential equations
  • ordinary differential equations
  • stochastic differential equations
  • fractional differential equations
  • fractional calculus
  • inverse and ill-posed problems
  • regularization methods
  • numerical methods
  • multigrid methods
  • wavelet methods
  • homotopy methods
  • structure-preserving methods
  • artificial intelligence
  • deep learning
  • reinforcement learning
  • compact radial basis function approximations
  • approximations based on neural networks
  • node layouts for irregular domains
  • multi-asset option pricing problems
  • numerical methods for matrix functions
  • iterative methods for the solution of nonlinear equations
  • Schulz-type iterative method for generalized matrix inversion
  • biostatistics and pattern recognition
  • combination counting
  • separation theory
  • information security
  • fractional Fourier transform and its applications
  • interdisciplinary application of mathematics and other disciplines

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  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
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Further information on MDPI's Special Issue policies can be found here.

Published Papers (15 papers)

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16 pages, 668 KiB  
Article
Managing the Risk via the Chi-Squared Distribution in VaR and CVaR with the Use in Generalized Autoregressive Conditional Heteroskedasticity Model
by Fazlollah Soleymani, Qiang Ma and Tao Liu
Mathematics 2025, 13(9), 1410; https://doi.org/10.3390/math13091410 - 25 Apr 2025
Abstract
This paper develops a framework for quantifying risk by integrating analytical derivations of Value at Risk (VaR) and Conditional VaR (CVaR) under the chi-squared distribution with empirical modeling via Generalized Autoregressive Conditional Heteroskedasticity (GARCH) processes. We first establish closed-form expressions for VaR and [...] Read more.
This paper develops a framework for quantifying risk by integrating analytical derivations of Value at Risk (VaR) and Conditional VaR (CVaR) under the chi-squared distribution with empirical modeling via Generalized Autoregressive Conditional Heteroskedasticity (GARCH) processes. We first establish closed-form expressions for VaR and CVaR under the chi-squared distribution, leveraging properties of the inverse regularized gamma function and its connection to the quantile of the distribution. We evaluate the proposed framework across multiple time windows to assess its stability and sensitivity to market regimes. Empirical results demonstrate the chi-squared-based VaR and CVaR, when coupled with GARCH volatility forecasts, particularly during periods of heightened market volatility. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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21 pages, 1213 KiB  
Article
A Model of Effector–Tumor Cell Interactions Under Chemotherapy: Bifurcation Analysis
by Rubayyi T. Alqahtani
Mathematics 2025, 13(7), 1032; https://doi.org/10.3390/math13071032 - 22 Mar 2025
Viewed by 212
Abstract
This paper studies the dynamic behavior of a three-dimensional mathematical model of effector–tumor cell interactions that incorporates the impact of chemotherapy. The well-known logistic function is used to model tumor growth. Elementary concepts of singularity theory are used to classify the model steady-state [...] Read more.
This paper studies the dynamic behavior of a three-dimensional mathematical model of effector–tumor cell interactions that incorporates the impact of chemotherapy. The well-known logistic function is used to model tumor growth. Elementary concepts of singularity theory are used to classify the model steady-state equilibria. I show that the model can predict hysteresis, isola/mushroom, and pitchfork singularities. Useful branch sets in terms of model parameters are constructed to delineate the domains of such singularities. I examine the effect of chemotherapy on bifurcation solutions, and I discuss the efficiency of chemotherapy treatment. I also show that the model cannot predict a periodic behavior for any model parameters. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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23 pages, 803 KiB  
Article
Efficient Scalar Multiplication of ECC Using Lookup Table and Fast Repeating Point Doubling
by Fu-Jung Kan, Yan-Haw Chen, Jeng-Jung Wang and Chong-Dao Lee
Mathematics 2025, 13(6), 924; https://doi.org/10.3390/math13060924 - 11 Mar 2025
Viewed by 502
Abstract
Reducing the computation time of scalar multiplication for elliptic curve cryptography is a significant challenge. This study proposes an efficient scalar multiplication method for elliptic curves over finite fields GF(2m). The proposed method first converts the scalar [...] Read more.
Reducing the computation time of scalar multiplication for elliptic curve cryptography is a significant challenge. This study proposes an efficient scalar multiplication method for elliptic curves over finite fields GF(2m). The proposed method first converts the scalar into a binary number. Then, using Horner’s rule, the binary number is divided into fixed-length bit-words. Each bit-word undergoes repeating point doubling, which can be precomputed. However, repeating point doubling typically involves numerous inverse operations. To address this, significant effort has been made to develop formulas that minimize the number of inverse operations. With the proposed formula, regardless of how many times the operation is repeated, only a single inverse operation is required. Over GF(2m), the proposed method for scalar multiplication outperforms the sliding window method, which is currently regarded as the fastest available. However, the introduced formulas require more multiplications, squares, and additions. To reduce these operations, we further optimize the square operations; however, this introduces a trade-off between computation time and memory size. These challenges are key areas for future improvement. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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17 pages, 12148 KiB  
Article
Numerical Simulation for the Wave of the Variable Coefficient Nonlinear Schrödinger Equation Based on the Lattice Boltzmann Method
by Huimin Wang, Hengjia Chen and Ting Li
Mathematics 2024, 12(23), 3807; https://doi.org/10.3390/math12233807 - 1 Dec 2024
Cited by 1 | Viewed by 788
Abstract
The variable coefficient nonlinear Schrödinger equation has a wide range of applications in various research fields. This work focuses on the wave propagation based on the variable coefficient nonlinear Schrödinger equation and the variable coefficient fractional order nonlinear Schrödinger equation. Due to the [...] Read more.
The variable coefficient nonlinear Schrödinger equation has a wide range of applications in various research fields. This work focuses on the wave propagation based on the variable coefficient nonlinear Schrödinger equation and the variable coefficient fractional order nonlinear Schrödinger equation. Due to the great challenge of accurately solving such problems, this work considers numerical simulation research on this type of problem. We innovatively consider using a mesoscopic numerical method, the lattice Boltzmann method, to study this type of problem, constructing lattice Boltzmann models for these two types of equations, and conducting numerical simulations of wave propagation. Error analysis was conducted on the model, and the convergence of the model was numerical validated. By comparing it with other classic schemes, the effectiveness of the model has been verified. The results indicate that lattice Boltzmann method has demonstrated advantages in both computational accuracy and time consumption. This study has positive significance for the fields of applied mathematics, nonlinear optics, and computational fluid dynamics. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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14 pages, 1614 KiB  
Article
Solving Nonlinear Equation Systems via a Steffensen-Type Higher-Order Method with Memory
by Shuai Wang, Haomiao Xian, Tao Liu and Stanford Shateyi
Mathematics 2024, 12(23), 3655; https://doi.org/10.3390/math12233655 - 22 Nov 2024
Viewed by 709
Abstract
This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The [...] Read more.
This article introduces a multi-step solver for sets of nonlinear equations. To achieve this, we consider and develop a multi-step Steffensen-type method without memory, which does not require evaluations of the Fréchet derivatives, and subsequently extend it to a method with memory. The resulting order is 5+2, utilizing the identical number of functional evaluations as the solver without memory, thereby demonstrating a higher computational index of efficiency. Finally, we illustrate the advantages of the proposed scheme with memory through various test problems. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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30 pages, 577 KiB  
Article
Impulsive Discrete Runge–Kutta Methods and Impulsive Continuous Runge–Kutta Methods for Nonlinear Differential Equations with Delayed Impulses
by Gui-Lai Zhang, Zhi-Yong Zhu, Yu-Chen Wang and Chao Liu
Mathematics 2024, 12(19), 3002; https://doi.org/10.3390/math12193002 - 26 Sep 2024
Viewed by 650
Abstract
In this paper, we study the asymptotical stability of the exact solutions of nonlinear impulsive differential equations with the Lipschitz continuous function f(t,x) for the dynamic system and for the impulsive term Lipschitz continuous delayed functions Ik [...] Read more.
In this paper, we study the asymptotical stability of the exact solutions of nonlinear impulsive differential equations with the Lipschitz continuous function f(t,x) for the dynamic system and for the impulsive term Lipschitz continuous delayed functions Ik. In order to obtain numerical methods with a high order of convergence and that are capable of preserving the asymptotical stability of the exact solutions of these equations, impulsive discrete Runge–Kutta methods and impulsive continuous Runge–Kutta methods are constructed, respectively. For these different types of numerical methods, different convergence results are obtained and the sufficient conditions for asymptotical stability of these numerical methods are also obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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17 pages, 4852 KiB  
Article
Nonlinear Complex Wave Excitations in (2+1)-Dimensional Klein–Gordon Equation Investigated by New Wave Transformation
by Guojiang Wu, Yong Guo and Yanlin Yu
Mathematics 2024, 12(18), 2867; https://doi.org/10.3390/math12182867 - 14 Sep 2024
Viewed by 761
Abstract
The Klein–Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method [...] Read more.
The Klein–Gordon equation plays an important role in mathematical physics, such as plasma and, condensed matter physics. Exploring its exact solution helps us understand its complex nonlinear wave phenomena. In this paper, we first propose a new extended Jacobian elliptic function expansion method for constructing rich exact periodic wave solutions of the (2+1)-dimensional Klein–Gordon equation. Then, we introduce a novel wave transformation for constructing nonlinear complex waves. To demonstrate the effectiveness of this method, we numerically simulated several sets of complex wave structures, which indicate new types of complex wave phenomena. The results show that this method is simple and effective for constructing rich exact solutions and complex nonlinear wave phenomena to nonlinear equations. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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19 pages, 504 KiB  
Article
Euler Method for a Class of Linear Impulsive Neutral Differential Equations
by Gui-Lai Zhang, Yang Sun, Ya-Xin Zhang and Chao Liu
Mathematics 2024, 12(18), 2833; https://doi.org/10.3390/math12182833 - 12 Sep 2024
Viewed by 1019
Abstract
This paper presents a new numerical scheme for a class of linear impulsive neutral differential equations with constant coefficients based on the Euler method. We rigorously establish the first-order convergence of the proposed numerical approach. Additionally, the asymptotical stability of the exact solutions [...] Read more.
This paper presents a new numerical scheme for a class of linear impulsive neutral differential equations with constant coefficients based on the Euler method. We rigorously establish the first-order convergence of the proposed numerical approach. Additionally, the asymptotical stability of the exact solutions and numerical solutions of impulsive neutral differential equations are studied. To substantiate our findings, two illustrative examples are provided, demonstrating the theoretical conclusions of this paper. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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21 pages, 499 KiB  
Article
Identification of Time-Wise Thermal Diffusivity, Advection Velocity on the Free-Boundary Inverse Coefficient Problem
by M. S. Hussein, Taysir E. Dyhoum, S. O. Hussein and Mohammed Qassim
Mathematics 2024, 12(17), 2629; https://doi.org/10.3390/math12172629 - 24 Aug 2024
Viewed by 1104
Abstract
This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved [...] Read more.
This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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22 pages, 4890 KiB  
Article
An Improved Three-Term Conjugate Gradient Algorithm for Constrained Nonlinear Equations under Non-Lipschitz Conditions and Its Applications
by Dandan Li, Yong Li and Songhua Wang
Mathematics 2024, 12(16), 2556; https://doi.org/10.3390/math12162556 - 19 Aug 2024
Viewed by 1088
Abstract
This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search [...] Read more.
This paper proposes an improved three-term conjugate gradient algorithm designed to solve nonlinear equations with convex constraints. The key features of the proposed algorithm are as follows: (i) It only requires that nonlinear equations have continuous and monotone properties; (ii) The designed search direction inherently ensures sufficient descent and trust-region properties, eliminating the need for line search formulas; (iii) Global convergence is established without the necessity of the Lipschitz continuity condition. Benchmark problem numerical results illustrate the proposed algorithm’s effectiveness and competitiveness relative to other three-term algorithms. Additionally, the algorithm is extended to effectively address the image denoising problem. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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21 pages, 14010 KiB  
Article
A Time-Series Feature-Extraction Methodology Based on Multiscale Overlapping Windows, Adaptive KDE, and Continuous Entropic and Information Functionals
by Antonio Squicciarini, Elio Valero Toranzo and Alejandro Zarzo
Mathematics 2024, 12(15), 2396; https://doi.org/10.3390/math12152396 - 31 Jul 2024
Viewed by 1280
Abstract
We propose a new methodology to transform a time series into an ordered sequence of any entropic and information functionals, providing a novel tool for data analysis. To achieve this, a new algorithm has been designed to optimize the Probability Density Function (PDF) [...] Read more.
We propose a new methodology to transform a time series into an ordered sequence of any entropic and information functionals, providing a novel tool for data analysis. To achieve this, a new algorithm has been designed to optimize the Probability Density Function (PDF) associated with a time signal in the context of non-parametric Kernel Density Estimation (KDE). We illustrate the applicability of this method for anomaly detection in time signals. Specifically, our approach combines a non-parametric kernel density estimator with overlapping windows of various scales. Regarding the parameters involved in the KDE, it is well-known that bandwidth tuning is crucial for the kernel density estimator. To optimize it for time-series data, we introduce an adaptive solution based on Jensen–Shannon divergence, which adjusts the bandwidth for each window length to balance overfitting and underfitting. This solution selects unique bandwidth parameters for each window scale. Furthermore, it is implemented offline, eliminating the need for online optimization for each time-series window. To validate our methodology, we designed a synthetic experiment using a non-stationary signal generated by the composition of two stationary signals and a modulation function that controls the transitions between a normal and an abnormal state, allowing for the arbitrary design of various anomaly transitions. Additionally, we tested the methodology on real scalp-EEG data to detect epileptic crises. The results show our approach effectively detects and characterizes anomaly transitions. The use of overlapping windows at various scales significantly enhances detection ability, allowing for the simultaneous analysis of phenomena at different scales. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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17 pages, 648 KiB  
Article
Quasi-Analytical Solution of Kepler’s Equation as an Explicit Function of Time
by A. N. Beloiarov, V. A. Beloiarov, R. C. Cruz-Gómez, C. O. Monzón and J. L. Romero
Mathematics 2024, 12(13), 2108; https://doi.org/10.3390/math12132108 - 4 Jul 2024
Cited by 1 | Viewed by 1104
Abstract
Although Kepler’s laws can be empirically proven by applying Newton’s laws to the dynamics of two particles attracted by gravitational interaction, an explicit formula for the motion as a function of time remains undefined. This paper proposes a quasi-analytical solution to address this [...] Read more.
Although Kepler’s laws can be empirically proven by applying Newton’s laws to the dynamics of two particles attracted by gravitational interaction, an explicit formula for the motion as a function of time remains undefined. This paper proposes a quasi-analytical solution to address this challenge. It approximates the real dynamics of celestial bodies with a satisfactory degree of accuracy and minimal computational cost. This problem is closely related to Kepler’s equation, as solving the equations of motion as a function of time also provides a solution to Kepler’s equation. The results are presented for each planet of the solar system, including Pluto, and the solution is compared against real orbits. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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17 pages, 357 KiB  
Article
Two Schemes of Impulsive Runge–Kutta Methods for Linear Differential Equations with Delayed Impulses
by Gui-Lai Zhang and Chao Liu
Mathematics 2024, 12(13), 2075; https://doi.org/10.3390/math12132075 - 2 Jul 2024
Cited by 1 | Viewed by 1045
Abstract
In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case [...] Read more.
In this paper, two different schemes of impulsive Runge–Kutta methods are constructed for a class of linear differential equations with delayed impulses. One scheme is convergent of order p if the corresponding Runge–Kutta method is p order. Another one in the general case is only convergent of order 1, but it is more concise and may suit for more complex differential equations with delayed impulses. Moreover, asymptotical stability conditions for the exact solution and numerical solutions are obtained, respectively. Finally, some numerical examples are provided to confirm the theoretical results. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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20 pages, 9523 KiB  
Article
Q-Sorting: An Algorithm for Reinforcement Learning Problems with Multiple Cumulative Constraints
by Jianfeng Huang, Guoqiang Lu, Yi Li and Jiajun Wu
Mathematics 2024, 12(13), 2001; https://doi.org/10.3390/math12132001 - 28 Jun 2024
Viewed by 1070
Abstract
This paper proposes a method and an algorithm called Q-sorting for reinforcement learning (RL) problems with multiple cumulative constraints. The primary contribution is a mechanism for dynamically determining the focus of optimization among multiple cumulative constraints and the objective. Executed actions are picked [...] Read more.
This paper proposes a method and an algorithm called Q-sorting for reinforcement learning (RL) problems with multiple cumulative constraints. The primary contribution is a mechanism for dynamically determining the focus of optimization among multiple cumulative constraints and the objective. Executed actions are picked through a procedure with two steps: first filter out actions potentially breaking the constraints, and second sort the remaining ones according to the Q values of the focus in descending order. The algorithm was originally developed upon the classic tabular value representation and episodic setting of RL, but the idea can be extended and applied to other methods with function approximation and discounted setting. Numerical experiments are carried out on the adapted Gridworld and the motor speed synchronization problem, both with one and two cumulative constraints. Simulation results validate the effectiveness of the proposed Q-sorting in that cumulative constraints are honored both during and after the learning process. The advantages of Q-sorting are further emphasized through comparison with the method of lumped performances (LP), which takes constraints into account through weighting parameters. Q-sorting outperforms LP in both ease of use (unnecessity of trial and error to determine values of the weighting parameters) and performance consistency (6.1920 vs. 54.2635 rad/s for the standard deviation of the cumulative performance index over 10 repeated simulation runs). It has great potential for practical engineering use. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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12 pages, 629 KiB  
Article
An Efficient Iterative Approach for Hermitian Matrices Having a Fourth-Order Convergence Rate to Find the Geometric Mean
by Tao Liu, Ting Li, Malik Zaka Ullah, Abdullah Khamis Alzahrani and Stanford Shateyi
Mathematics 2024, 12(11), 1772; https://doi.org/10.3390/math12111772 - 6 Jun 2024
Viewed by 1145
Abstract
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth [...] Read more.
The target of this work is to present a multiplication-based iterative method for two Hermitian positive definite matrices to find the geometric mean. The method is constructed via the application of the matrix sign function. It is theoretically investigated that it has fourth order of convergence. The type of convergence is also discussed, which is global under an appropriate choice of the initial matrix. Numerical experiments are reported based on input matrices of different sizes as well as various stopping termination levels with comparisons to methods of the same nature and same number of matrix–matrix multiplications. The simulation results confirm the efficiency of the proposed scheme in contrast to its competitors of the same nature. Full article
(This article belongs to the Special Issue Advances in Computational Mathematics and Applied Mathematics)
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