Principal minors, Part II: The principal minor assignment problem |
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Authors: | Kent Griffin |
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Affiliation: | Mathematics Department, Washington State University, Pullman, WA 99164-3113, USA |
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Abstract: | The inverse problem of finding a matrix with prescribed principal minors is considered. A condition that implies a constructive algorithm for solving this problem will always succeed is presented. The algorithm is based on reconstructing matrices from their principal submatrices and Schur complements in a recursive manner. Consequences regarding the overdeterminancy of this inverse problem are examined, leading to a faster (polynomial time) version of the algorithmic construction. Care is given in the MATLAB® implementation of the algorithms regarding numerical stability and accuracy. |
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Keywords: | 15A29 93B55 15A15 65F40 |
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