Computing the nearest stable matrix pairs

Computing nearest stable matrix pairs

In this paper, we study the nearest stable matrix pair problem: given a square matrix pair (E,A), minimize the Frobenius norm of (∆E ,∆A) such that (E+∆E , A+∆A) is a stable matrix pair. We propose a reformulation of the problem with a simpler feasible set by introducing dissipative Hamiltonian (DH) matrix pairs: A matrix pair (E,A) is DH if A = (J −R)Q with skew-symmetric J , positive semidefi...

Computing the Nearest Correlation Matrix

Computing the Nearest Rank-Deficient Matrix Polynomial

Matrix polynomials appear in many areas of computational algebra, control systems theory, di‚erential equations, and mechanics, typically with real or complex coecients. Because of numerical error and instability, a matrix polynomial may appear of considerably higher rank (generically full rank), while being very close to a rank-de€cient matrix. “Close” is de€ned naturally under the Frobenius ...

Computing the Matrix Geometric Mean of Two HPD Matrices: A Stable Iterative Method

A new iteration scheme for computing the sign of a matrix which has no pure imaginary eigenvalues is presented. Then, by applying a well-known identity in matrix functions theory, an algorithm for computing the geometric mean of two Hermitian positive definite matrices is constructed. Moreover, another efficient algorithm for this purpose is derived free from the computation of principal matrix...

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 ...