THE PRODUCT-PRODUCT SINGULAR VALUE DECOMPOSITION OF MATRIX TRIPLETS

A new decomposition of a matrix triplet (A, B, C) corresponding to the singular value decomposition of the matrix product ABC is developed in this paper, which will be termed the Product-Product Singular Value Decomposition (PPSVD). An orthogonal variant of the decomposition which is more suitable for the purpose of numerical computation is also proposed. Some geometric and algebraic issues of the PPSVD, such as the variational and geometric interpretations, and uniqueness properties are discussed. A numerical algorithm for stably computing the PPSVD is given based on the implicit Kogbetliantz technique. A numerical example is outlined to demonstrate the accuracy of the proposed algorithm.