Convergence of Gradient-Based Block Coordinate Descent Algorithms for Nonorthogonal Joint Approximate Diagonalization of Matrices

We propose a gradient-based block coordinate descent (BCD-G) framework to solve the joint approximate diagonalization of matrices defined on product complex Stiefel manifold and special linear group. Instead cyclic fashion, we choose optimization based Riemannian gradient. To update first variable in manifold, use well-known line search method. second group, four different kinds elementary transformations, construct three classes, GLU, GQU GU, then get BCD-G algorithms, BCD-GLU, BCD-GQU BCD-GU. establish global convergence weak these algorithms using Łojasiewicz gradient inequality under assumption that iterates are bounded. also Jacobi-type As case, GLU classes focus Jacobi-GLU Jacobi-GQU their as well. All results described this paper apply real case.