Hanbook Series Linear Algebra

Numerische Mathematik

, Volume 27, Issue 1, pp 95-109

First online:

Decomposition of a symmetric matrix

  • James R. BunchAffiliated withDepartment of Mathematics, University of California
  • , Linda KaufmanAffiliated withBell Laboratories
  • , Beresford N. ParlettAffiliated withDepartment of Mathematics and Department of Electrical Engineering and Computer Science, University of California

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An algorithm is presented to compute a triangular factorization and the inertia of a symmetric matrix. The algorithm is stable even when the matrix is not positive definite and is as fast as Cholesky. Programs for solving associated systems of linear equations are included.