AN ALGEBRAIC APPROACH TO NONORTHOGONAL GENERAL JOINT BLOCK DIAGONALIZATION

作者：Cai, Yunfeng^*; Liu, Chengyu

来源：SIAM Journal on Matrix Analysis and Applications, 2017, 38(1): 50-71.

DOI：10.1137/16M1080756

• joint block diagonalization
• tensor decomposition
• independent component analysis

The exact/approximate nonorthogonal general joint block diagonalization (NOGJBD) problem of a given real matrix set A = {A(i)}(i=1)(m) is to find a nonsingular matrix W epsilon R-nxn (diagonalizer) such that W(T)A(i)W for i = 1, 2,..., m are all exactly/approximately block diagonal matrices with the same diagonal block structure and with as many diagonal blocks as possible. In this paper, we show that a solution to the exact/approximate NOGJBD problem can be obtained by finding the exact/approximate solutions to the system of linear equations A(i)Z = Z(T)A(i) for i = 1,..., m, followed by a block diagonalization of Z via similarity transformation. A necessary and sufficient condition for the equivalence of the solutions to the exact NOGJBD problem is established. Two numerical methods are proposed to solve the NOGJBD problem, and numerical examples are presented to show the merits of the proposed methods.

• 出版日期2017
• 单位北京大学