Computational geometry of positive definiteness

Tutkimustuotos: Lehtiartikkelivertaisarvioitu

Tutkijat

  • Marko Huhtanen
  • Otto Seiskari

Organisaatiot

Kuvaus

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.

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut1562-1578
Sivumäärä17
JulkaisuLinear Algebra and Its Applications
Vuosikerta437
Numero7
TilaJulkaistu - 1 lokakuuta 2012
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 12920396