Principal minors, Part II: The principal minor assignment problem
نویسندگان
چکیده
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. © 2006 Elsevier Inc. All rights reserved. AMS classification: 15A29; 93B55; 15A15; 65F40
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