On near and the nearest correlation matrix

Computing the Nearest Correlation Matrix

Bounds for the Distance to the Nearest Correlation Matrix

In a wide range of practical problems correlation matrices are formed in such a way that, while symmetry and a unit diagonal are assured, they may lack semidefiniteness. We derive a variety of new upper bounds for the distance from an arbitrary symmetric matrix to the nearest correlation matrix. The bounds are of two main classes: those based on the eigensystem and those based on a modified Cho...

Computing the Nearest Correlation Matrix using Difference Map Algorithm

The difference map algorithm (DMA) is originally designed to find the global optimal solution to nonconvex problems. The main feature of DMA is that it can avoid the stagnation, (which always occurs when applying the alternating projection method (APM) on nonconvex problems so that APM is trapped at local minimized point and fail to find the global optimal solution.) and converge to the global ...

Computing the Nearest Correlation Matrix—A Problem from Finance

Given a symmetric matrix what is the nearest correlation matrix, that is, the nearest symmetric positive semidefinite matrix with unit diagonal? This problem arises in the finance industry, where the correlations are between stocks. For distance measured in two weighted Frobenius norms we characterize the solution using convex analysis. We show how the modified alternating projections method ca...

A preconditioned Newton algorithm for the nearest correlation matrix

Various methods have been developed for computing the correlation matrix nearest in the Frobenius norm to a given matrix. We focus on a quadratically convergent Newton algorithm recently derived by Qi and Sun. Various improvements to the efficiency and reliability of the algorithm are introduced. Several of these relate to the linear algebra: the Newton equations are solved by minres instead of...