Inverse of a symmetric positive-definite matrixAdelchi Azzalini
If a matrix is symmetric and positive definite, determine if it is invertible and if its inverse matrix is symmetric and positive definite. I know that "if a matrix is symmetric and positive definite, then its inverse matrix is also positive definite", based on a theorem. But I am not su...
In this paper generalized inverse eigenvalue problems of bi-anti-symmetric matrix and optimal approximation are discussed;the expression of general solution and optimal approximation solution are attained,and an arithmetic and a numerical examples are given. 矩阵逆特征值问题广泛应用于自动控制、经济、振...
The calculation of some of the elements of the inverse of a symmetric positive definite matrix occurs in statistical computations when some of the variances, covariances, or correlations coefficients are desired. The efficient computation of these elements is discussed and Fortran codes are given for...
1.Method for judginginverse M-matrixand its parallel algorithm;一种基于并行算法的逆M矩阵的判定方法 2.A necessary condition for the completion of a partially symmetricinverse M-matrix;部分对称逆M矩阵完备化的必要条件 3.The Property and Judgment of Inverse M-Matrixes;逆M矩阵的性质及其判断 ...
symmetric and positive definite matrices. Positive definite means itsdeterminant is strictly positive. In fact, we can assume here thateveryone's determinant is bounded away from zero (even the inverses); thus,condition numbers, floating point precision, overflow, etc. are ...
1.Method for judginginverse M-matrixand its parallel algorithm;一种基于并行算法的逆M矩阵的判定方法 2.A necessary condition for the completion of a partially symmetricinverse M-matrix;部分对称逆M矩阵完备化的必要条件 3.The Property and Judgment of Inverse M-Matrixes;逆M矩阵的性质及其判断 ...
1.Method for judginginverse M-matrixand its parallel algorithm;一种基于并行算法的逆M矩阵的判定方法 2.A necessary condition for the completion of a partially symmetricinverse M-matrix;部分对称逆M矩阵完备化的必要条件 3.The Property and Judgment of Inverse M-Matrixes;逆M矩阵的性质及其判断 ...
This produces a symmetric positive-definite matrix: Hred=MTM+αJpp. (3.7) Thus, we are able to draw upon the classical Gauss–Newton method. In this paper, we will use a preconditioned conjugate gradient (PCG) method to solve Eq. (3.5). 3.2 A preconditioned Krylov subspace method for...
The geometric perspective however connects sign properties of entries of inverses of a symmetric positive definite matrix to the dihedral angle properties of an underlying simplex, and enables an explicit visualization of how these angles and signs can be manipulated. This will serve to formulate ...