Positive definite matrix approximation with condition number constraint
Positive definite matrix approximation with condition number constraint
复制标题
DOI：
10.1007/s11590-013-0632-7
复制
发表时间：
2014-03-01
影响因子：
1.6
通讯作者：
Nakata, Kazuhide
中科院分区：
文献类型：
--
作者：
Tanaka, Mirai;Nakata, Kazuhide
带条件数约束的正定矩阵逼近是求条件数小于给定常数的最近邻正定矩阵的优化问题。我们证明了当我们使用一个酉相似不变范数作为度量时，这个问题可以转化为一个更简单的问题。当我们使用Ky Fan p-k范数时，我们可以特别地将其转化为单变量分段凸优化问题。给出了度量为谱范数和迹范数的问题的解析解。
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.