Computational geometry of positive definiteness

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Computational geometry of positive definiteness. / Huhtanen, Marko; Seiskari, Otto.

In: Linear Algebra and Its Applications, Vol. 437, No. 7, 01.10.2012, p. 1562-1578.

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Huhtanen, Marko ; Seiskari, Otto. / Computational geometry of positive definiteness. In: Linear Algebra and Its Applications. 2012 ; Vol. 437, No. 7. pp. 1562-1578.

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@article{e802ec01d6504cf68cf8b19d65fffc82,
title = "Computational geometry of positive definiteness",
abstract = "In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as those of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task becomes computational geometric for the joint numerical range in a natural way. The Hermitian element of the Frobenius norm one with the maximal least eigenvalue is found. To this end, extreme eigenvalue computations are combined with ellipsoid and perceptron algorithms.",
keywords = "Computational geometry, Convex analysis, Eigenvalue optimization, Hermitian matrix subspace, Joint numerical range, Positive definiteness",
author = "Marko Huhtanen and Otto Seiskari",
year = "2012",
month = "10",
day = "1",
doi = "10.1016/j.laa.2012.05.002",
language = "English",
volume = "437",
pages = "1562--1578",
journal = "Linear Algebra and Its Applications",
issn = "0024-3795",
number = "7",

}

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TY - JOUR

T1 - Computational geometry of positive definiteness

AU - Huhtanen, Marko

AU - Seiskari, Otto

PY - 2012/10/1

Y1 - 2012/10/1

N2 - In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as those of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task becomes computational geometric for the joint numerical range in a natural way. The Hermitian element of the Frobenius norm one with the maximal least eigenvalue is found. To this end, extreme eigenvalue computations are combined with ellipsoid and perceptron algorithms.

AB - In matrix computations, such as in factoring matrices, Hermitian and, preferably, positive definite elements are occasionally required. Related problems can often be cast as those of existence of respective elements in a matrix subspace. For two dimensional matrix subspaces, first results in this regard are due to Finsler. To assess positive definiteness in larger dimensional cases, the task becomes computational geometric for the joint numerical range in a natural way. The Hermitian element of the Frobenius norm one with the maximal least eigenvalue is found. To this end, extreme eigenvalue computations are combined with ellipsoid and perceptron algorithms.

KW - Computational geometry

KW - Convex analysis

KW - Eigenvalue optimization

KW - Hermitian matrix subspace

KW - Joint numerical range

KW - Positive definiteness

UR - http://www.scopus.com/inward/record.url?scp=84863981699&partnerID=8YFLogxK

U2 - 10.1016/j.laa.2012.05.002

DO - 10.1016/j.laa.2012.05.002

M3 - Article

VL - 437

SP - 1562

EP - 1578

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

IS - 7

ER -

ID: 12920396