Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition

John R. Singler

doi:10.1109/ACC.2008.4586502

Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition

John R. Singler

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

Original language	American English
Journal	Proceedings of the 2008 American Control Conference
DOIs	https://doi.org/10.1109/ACC.2008.4586502
State	Published - Jun 1 2008

Keywords

Approximation Theory
Infinite Dimensional Problems
Lyapunov Methods
Matrix Algebra
Matrix Approximations
Proper Orthogonal Decomposition

Disciplines

Mathematics
Statistics and Probability

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title = "Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition",

abstract = " We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.",

keywords = "Approximation Theory, Infinite Dimensional Problems, Lyapunov Methods, Matrix Algebra, Matrix Approximations, Proper Orthogonal Decomposition",

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N2 - We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

AB - We present an algorithm to approximate the solution Z of a stable Lyapunov equation AZ + ZA* + BB* = 0 using proper orthogonal decomposition (POD). This algorithm is applicable to large-scale problems and certain infinite dimensional problems as long as the rank of B is relatively small. In the infinite dimensional case, the algorithm does not require matrix approximations of the operators A and B. POD is used in a systematic way to provide convergence theory and simple a priori error bounds.

KW - Approximation Theory

KW - Infinite Dimensional Problems

KW - Lyapunov Methods

KW - Matrix Algebra

KW - Matrix Approximations

KW - Proper Orthogonal Decomposition

UR - https://scholarsmine.mst.edu/math_stat_facwork/659

U2 - 10.1109/ACC.2008.4586502

DO - 10.1109/ACC.2008.4586502

M3 - Article

JO - Proceedings of the 2008 American Control Conference

JF - Proceedings of the 2008 American Control Conference

ER -

Approximate Low Rank Solutions of Lyapunov Equations Via Proper Orthogonal Decomposition

Abstract

Keywords

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