Polynomials and lemniscates of indefiniteness

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Polynomials and lemniscates of indefiniteness. / Huhtanen, Marko; Nevanlinna, Olavi.

julkaisussa: Numerische Mathematik, Vuosikerta 133, Nro 2, 06.2016, s. 233-253.

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Huhtanen, Marko ; Nevanlinna, Olavi. / Polynomials and lemniscates of indefiniteness. Julkaisussa: Numerische Mathematik. 2016 ; Vuosikerta 133, Nro 2. Sivut 233-253.

Bibtex - Lataa

@article{18c4bd72bef34e08a03ba6b964ec20ff,
title = "Polynomials and lemniscates of indefiniteness",
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.",
keywords = "POTENTIAL-THEORY, NORMAL OPERATORS, APPROXIMATION, ITERATIONS, LENGTH",
author = "Marko Huhtanen and Olavi Nevanlinna",
year = "2016",
month = "6",
doi = "10.1007/s00211-015-0745-2",
language = "English",
volume = "133",
pages = "233--253",
journal = "Numerische Mathematik",
issn = "0029-599X",
number = "2",

}

RIS - Lataa

TY - JOUR

T1 - Polynomials and lemniscates of indefiniteness

AU - Huhtanen, Marko

AU - Nevanlinna, Olavi

PY - 2016/6

Y1 - 2016/6

N2 - 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.

AB - 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.

KW - POTENTIAL-THEORY

KW - NORMAL OPERATORS

KW - APPROXIMATION

KW - ITERATIONS

KW - LENGTH

UR - http://link.springer.com/article/10.1007%2Fs00211-015-0745-2

U2 - 10.1007/s00211-015-0745-2

DO - 10.1007/s00211-015-0745-2

M3 - Article

VL - 133

SP - 233

EP - 253

JO - Numerische Mathematik

JF - Numerische Mathematik

SN - 0029-599X

IS - 2

ER -

ID: 1980077