Computational matrix representation modules for linear operators with explicit constructions for a class of Lie operators
type: Item
instance of: scholarly article
title: Computational matrix representation modules for linear operators with explicit constructions for a class of Lie operators
zbMATH Open document ID: 0932.65052
DOI: 10.1016/S0377-0427(98)00088-0
author: Jyun-Horng Fu
author: David F. Miller
published in: Journal of Computational and Applied Mathematics
publication date: 1999-08-22T00:00:00Z
review text: The authors develop a procedure for constructing matrix representations for a class of linear operators on finite-dimensional spaces. First serial number functions for locating basis monomials in the linear space of homogeneous polynomials of fixed degree, ordered under structural lexicographic are presented. Next basic lemmas describing the modular structure of matrix representations for operators constructed conically from elementary operators are presented. Using these results, explicit matrix representations are then given for the Lie derivative and Lie-Poisson bracket operators defined on spaces of homogeneous polynomials. In particular, they are comprized of blocks obtained as Kronecker sums of modular components, each corresponding to specific Jordan blocks. At an implementation level, recursive programming is applied to construct these modular components explicitly. The results are also applied to computing power series approximations for the center manifold of a dynamical system. In this setting, the linear operator of interest is parameterized by two matrices, a generalization of the Lie-Poisson bracket.
Mathematics Subject Classification ID: 65F30
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65P10
zbMATH DE Number: 1326549
zbMATH Keywords: matrix representations
zbMATH Keywords: linear operators
zbMATH Keywords: Lie derivative
zbMATH Keywords: Lie-Poisson bracket operators
zbMATH Keywords: Jordan blocks
zbMATH Keywords: recursive programming
zbMATH Keywords: center manifold
zbMATH Keywords: dynamical system
reviewed by: Prem Narain
MaRDI profile type: Publication
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full work available at URL: s0377-0427(98)00088-0
OpenAlex ID: W2024544521
description: scientific article; zbMATH DE number 1326549