Polynomials and lemniscates of indefiniteness

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Abstract

For a large indefinite linear system, there exists the option to directly precondition for the normal equations. Matrix nearness problems are formulated to assess the attractiveness of this alternative. Polynomial preconditioning leads to polynomial approximation problems involving lemniscate-like sets, both in the plane and in C-nxn. A natural matrix analytic extension for lemniscates is introduced. Operator theoretically one is concerned with polynomial unitarity and associated factorizations for the inverse. For the speed of convergence and lemniscate asymptotics, the notion of quasilemniscate arises. In the L-2-norm algorithms for solving the problem are devised.

Details

Original languageEnglish
Pages (from-to)233-253
Number of pages21
JournalNumerische Mathematik
Volume133
Issue number2
Publication statusPublished - Jun 2016
MoE publication typeA1 Journal article-refereed

    Research areas

  • POTENTIAL-THEORY, NORMAL OPERATORS, APPROXIMATION, ITERATIONS, LENGTH

ID: 1980077