Successive Projection Method for Well-Conditioned Matrix Approximation Problems
Successive Projection Method for Well-Conditioned Matrix Approximation Problems
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DOI：
10.1109/lsp.2014.2303153
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发表时间：
2014-01
影响因子：
3.9
通讯作者：
Mirai Tanaka;K. Nakata
中科院分区：
文献类型：
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作者：
Mirai Tanaka;K. Nakata
在包括信号处理在内的广泛领域中，通常要求矩阵具有良好的条件。给出了求同时满足条件数约束和符号约束的最近正定矩阵或最近相关矩阵的问题。这两个问题都可以看作是寻找条件数约束对应的封闭凸锥与其他约束对应的凸多面体交点的投影问题。因此，我们可以应用连续投影法来求解这些问题，连续投影法是求解多个凸集交点投影的经典算法。数值结果表明，该算法有效地解决了上述问题。
Matrices are often required to be well-conditioned in a wide variety of areas including signal processing. Problems to find the nearest positive definite matrix or the nearest correlation matrix that simultaneously satisfy the condition number constraint and sign constraints are presented in this paper. Both problems can be regarded as those to find a projection to the intersection of the closed convex cone corresponding to the condition number constraint and the convex polyhedron corresponding to the other constraints. Thus, we can apply a successive projection method, which is a classical algorithm for finding the projection to the intersection of multiple convex sets, to these problems. The numerical results demonstrated that the algorithm effectively solved the problems.