Positive definite matrix approximation with condition number constraint |
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Authors: | Mirai Tanaka Kazuhide Nakata |
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Institution: | 1. 2-12-1-W9-60, Ookayama, Meguro-ku, Tokyo, 152-8552, Japan
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Abstract: | Positive definite matrix approximation with a condition number constraint is an optimization problem to find the nearest positive definite matrix whose condition number is smaller than a given constant. We demonstrate that this problem can be converted to a simpler one when we use a unitary similarity invariant norm as a metric. We can especially convert it to a univariate piecewise convex optimization problem when we use the Ky Fan p-k norm. We also present an analytical solution to the problem whose metric is the spectral norm and the trace norm. |
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