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Principal minors, Part I: A method for computing all the principal minors of a matrix

✍ Scribed by Kent Griffin; Michael J. Tsatsomeros

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 180 KB
Volume: 419
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.04.008

No coin nor oath required. For personal study only.

✦ Synopsis

An order O(2 n ) algorithm for computing all the principal minors of an arbitrary n × n complex matrix is motivated and presented, offering an improvement by a factor of n 3 over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a binary order. An implementation of the algorithm in MATLAB is also given and practical considerations are discussed and treated accordingly.

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