Computational geometry of positive definiteness

Marko Huhtanen*, Otto Seiskari

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1562-1578
Number of pages17
JournalLinear Algebra and Its Applications
Issue number7
Publication statusPublished - 1 Oct 2012
MoE publication typeA1 Journal article-refereed


  • Computational geometry
  • Convex analysis
  • Eigenvalue optimization
  • Hermitian matrix subspace
  • Joint numerical range
  • Positive definiteness


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