Numerical Methods for Scientific Computing

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

Deadline for manuscript submissions: 30 April 2025 | Viewed by 948

Special Issue Editors


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Guest Editor
Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan
Interests: tensor/matrix analysis and computations; optimization; theory and algorithms; numerical analysis and scientific computing

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Guest Editor
Department of Mathematics, The University of Tennessee, Knoxville, TN 37996, USA
Interests: computational and applied mathematics; numerical analysis; scientific computing; numerical solutions of partial differential equations; uncertainty quantification; fractional calculus; fractional/nonlocal differential equations; deep neural networks; high-dimensional computation

Special Issue Information

Dear Colleagues,

The Special Issue, “Numerical Methods for Scientific Computing”, focuses on the application and development of computational techniques for solving scientific problems and delves into various numerical methods employed in fields such as physics, engineering, mathematics, and more. The Special issue explores topics including numerical differential equations, numerical optimization, numerical linear algebra, numerical multilinear algebra, eigenvalue problems and nonlinear eigenvalue problems, and matrix and tensor approximation. The emphasis is placed on the theoretical foundations, algorithmic advancements, and practical applications of these numerical techniques. By addressing these areas, this Special Issue aims to contribute to the advancement of scientific computing and its interdisciplinary applications.

Prof. Dr. Ching-Sung Liu
Prof. Dr. Xiaobing Feng
Guest Editors

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Keywords

  • numerical methods
  • numerical differential equations
  • numerical optimization
  • numerical linear algebra
  • numerical multilinear algebra
  • eigenvalue problems
  • nonlinear eigenvalue problems
  • matrix approximation
  • tensor approximation

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Published Papers (1 paper)

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Research

14 pages, 324 KiB  
Article
An Inexact Noda Iteration for Computing the Smallest Eigenpair of a Large, Irreducible Monotone Matrix
by Ching-Sung Liu
Mathematics 2024, 12(16), 2546; https://doi.org/10.3390/math12162546 - 17 Aug 2024
Viewed by 699
Abstract
In this paper, we introduce an inexact Noda iteration method featuring inner and outer iterations for computing the smallest eigenvalue and corresponding eigenvector of an irreducible monotone matrix. The proposed method includes two primary relaxation steps designed to compute the smallest eigenvalue and [...] Read more.
In this paper, we introduce an inexact Noda iteration method featuring inner and outer iterations for computing the smallest eigenvalue and corresponding eigenvector of an irreducible monotone matrix. The proposed method includes two primary relaxation steps designed to compute the smallest eigenvalue and its associated eigenvector. These steps are influenced by specific relaxation factors, and we examine how these factors impact the convergence of the outer iterations. By applying two distinct relaxation factors to solve the inner linear systems, we demonstrate that the convergence can be globally linear or superlinear, contingent upon the relaxation factor used. Additionally, the relaxation factor affects the rate of convergence. The inexact Noda iterations we propose are structure-preserving and ensure the positivity of the approximate eigenvectors. Numerical examples are provided to demonstrate the practicality of the proposed method, consistently preserving the positivity of approximate eigenvectors. Full article
(This article belongs to the Special Issue Numerical Methods for Scientific Computing)
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