Wilkinson's inertia-revealing factorization and its application to sparse matrices

Alex Druinsky, Eyal Carlebach, Sivan Toledo

Research output: Contribution to journalArticlepeer-review


We propose a new inertia-revealing factorization for sparse symmetric matrices. The factorization scheme and the method for extracting the inertia from it were proposed in the 1960s for dense, banded, or tridiagonal matrices, but they have been abandoned in favor of faster methods. We show that this scheme can be applied to any sparse symmetric matrix and that the fill in the factorization is bounded by the fill in the sparse QR factorization of the same matrix (but is usually much smaller). We describe our serial proof-of-concept implementation and present experimental results, studying the method's numerical stability and performance.

Original languageEnglish
Article numbere2130
JournalNumerical Linear Algebra with Applications
Issue number2
StatePublished - Mar 2018


  • matrix inertia
  • sparse matrix factorization
  • symmetric indefinite matrices


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