PHSS Iterative Method for Solving Generalized Lyapunov Equations †
Abstract
:1. Introduction
2. The PHSS Iterative Method for the Generalized Lyapunov Equation
3. Inexact PHSS (IPHSS) Iterative Algorithm
Algorithm 1.(Inexact PHSS Algorithm) |
Let us give the initial value , and calculate the until the accuracy requirement is met.
|
4. Numerical Experiments
5. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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n | IHSS | IPHSS | ||||
---|---|---|---|---|---|---|
Iter | CPU | Res | Iter | CPU | Res | |
4 | 269 | 0.215 | 9.6357 × 10−7 | 4 | 0.070 | 7.4966 × 10−8 |
16 | 267 | 0.559 | 8.0967 × 10−7 | 4 | 0.077 | 1.6256 × 10−7 |
64 | 259 | 1.763 | 9.8830 × 10−7 | 5 | 0.169 | 8.1159 × 10−8 |
144 | 266 | 43.010 | 9.9025 × 10−7 | 5 | 0.792 | 1.5784 × 10−7 |
256 | 255 | 260.165 | 9.6540 × 10−7 | 5 | 4.029 | 2.0429 × 10−7 |
529 | 283 | 2502.291 | 9.2328 × 10−7 | 5 | 39.945 | 2.3134 × 10−7 |
1024 | — | — | — | 5 | 383.907 | 1.7833 × 10−7 |
n | IHSS | IPHSS | ||||
---|---|---|---|---|---|---|
Iter | CPU | Res | Iter | CPU | Res | |
64 | 24 | 0.413 | 6.9964 × 10−6 | 4 | 0.092 | 2.1691 × 10−8 |
128 | 21 | 1.757 | 9.0778 × 10−6 | 4 | 0.382 | 4.6206 × 10−8 |
256 | 20 | 12.432 | 9.3266 × 10−6 | 4 | 2.290 | 1.0216 × 10−7 |
512 | 19 | 109.701 | 9.8608 × 10−6 | 4 | 21.917 | 2.8474 × 10−7 |
1024 | 19 | 1382.280 | 8.3162 × 10−6 | 4 | 291.388 | 3.8898 × 10−7 |
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Li, S.-Y.; Shen, H.-L.; Shao, X.-H. PHSS Iterative Method for Solving Generalized Lyapunov Equations. Mathematics 2019, 7, 38. https://doi.org/10.3390/math7010038
Li S-Y, Shen H-L, Shao X-H. PHSS Iterative Method for Solving Generalized Lyapunov Equations. Mathematics. 2019; 7(1):38. https://doi.org/10.3390/math7010038
Chicago/Turabian StyleLi, Shi-Yu, Hai-Long Shen, and Xin-Hui Shao. 2019. "PHSS Iterative Method for Solving Generalized Lyapunov Equations" Mathematics 7, no. 1: 38. https://doi.org/10.3390/math7010038
APA StyleLi, S.-Y., Shen, H.-L., & Shao, X.-H. (2019). PHSS Iterative Method for Solving Generalized Lyapunov Equations. Mathematics, 7(1), 38. https://doi.org/10.3390/math7010038