*5.3. Computational Complexity*

The running-time comparison among the algorithms is summarized in Table 5. The experiment was conducted for the *DS* simulated data, which has 75 × 75 pixels, 224 bands, and 240 spectral signatures in the library. The algorithms ran on a desktop computer with 3.50-GHz Intel Core i5 processor and 8 GB of RAM. From the table, J-LASU was the slowest due to its high computational complexity.

For the complexity analysis, recall that *n*, *m*, *N*, and *mb* are the number of pixels, spectral signatures in the library, pixels in each LA band, and local endmembers, respectively. For each iteration of J-LASU, the computation of **X** and the SVD step in the computation of **V**3 incur the most cost. The complexity of **X** computation is due to the use of conjugate gradient solver, which costs O(*m*) per iteration. The conjugate gradient is a popular iterative technique for solving the system of linear equation **Ax** = **b**, where the matrix **A** must be symmetric possitive definite (SPD), large and sparse. The SVD step costs <sup>O</sup>(*m*2*b<sup>N</sup>*); however, this step is repeated as many times as the number of blocks (*B*) due to the sliding of the local block. Since *B* is calculated by *mn*/*mbN*, the total cost of **V**3 is O(*mbmn*), which is more complex than the computation of **X**. Hence, the overall complexity costs O(*mbmn*).

**Table 5.** Comparison of running times for *DS*-data experiment.

