Low-rank updates and divide-and-conquer methods for quadratic matrix equations

Kressner Daniel; Kurschner Patrick; Massei Stefano

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Low-rank updates and divide-and-conquer methods for quadratic matrix equations

机译：Low-rank updates and divide-and-conquer methods for quadratic matrix equations

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摘要

In this work, we consider two types of large-scale quadratic matrix equations: continuous-time algebraic Riccati equations, which play a central role in optimal and robust control, and unilateral quadratic matrix equations, which arise from stochastic processes on 2D lattices and vibrating systems. We propose a simple and fast way to update the solution to such matrix equations under low-rank modifications of the coefficients. Based on this procedure, we develop a divide-and-conquer method for quadratic matrix equations with coefficients that feature a specific type of hierarchical low-rank structure, which includes banded matrices. This generalizes earlier work on linear matrix equations. Numerical experiments indicate the advantages of our newly proposed method versus iterative schemes combined with hierarchical low-rank arithmetic.

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来源
《Microbiology and molecular biology reviews》 |2020年第2期|717-741|共25页
作者
Kressner Daniel; Kurschner Patrick; Massei Stefano;
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作者单位

EPF Lausanne, Lausanne, Switzerland;

Katholieke Univ Leuven, Dept Elect Engn ESAT STADIUS, Heverlee, Belgium;

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正文语种英语
中图分类微生物学;分子生物学;
关键词
Riccati equation; Unilateral quadratic matrix equation; Low-rank update; Divide-and-conquer; Hierarchical matrices;

Low-rank updates and divide-and-conquer methods for quadratic matrix equations

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