Solution of large scale algebraic matrix riccati equations by use of hierarchical matrices

In previous papers, a class of hierarchical matrices ([Hamiltonian (script capital H)]-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the [Hamiltonian (script capital H)]-matrix str...

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Published in:Computing 2003-04, Vol.70 (2), p.121-165
Main Authors: GRASEDYCK, L, HACKBUSCH, W, KHOROMSKIJ, B. N
Format: Article
Language:English
Subjects:
Algebra
Approximation
Exact sciences and technology
Mathematics
Multiplication & division
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Sparsity
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HACKBUSCH, W
KHOROMSKIJ, B. N
description In previous papers, a class of hierarchical matrices ([Hamiltonian (script capital H)]-matrices) is introduced which are data-sparse and allow an approximate matrix arithmetic of almost optimal complexity. Here, we investigate a new approach to exploit the [Hamiltonian (script capital H)]-matrix structure for the solution of large scale Lyapunov and Riccati equations as they typically arise for optimal control problems where the constraint is a partial differential equation of elliptic type. This approach leads to an algorithm of linear-logarithmic complexity in the size of the matrices.
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subjects Algebra
Approximation
Exact sciences and technology
Mathematics
Multiplication & division
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Partial differential equations
Partial differential equations, boundary value problems
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Sciences and techniques of general use
Sparsity
title Solution of large scale algebraic matrix riccati equations by use of hierarchical matrices
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