A constructive arbitrary-degree Kronecker product decomposition of tensors

A constructive arbitrary-degree Kronecker product decomposition of tensors

We propose the tensor Kronecker product singular value decomposition (TKPSVD) that decomposes a real k-way tensor A into a linear combination of tensor Kronecker products with an arbitrary number of d factors A = ∑R j=1 σj A (d) j ⊗ · · · ⊗ A (1) j . We generalize the matrix Kronecker product to tensors such that each factor A j in the TKPSVD is a k-way tensor. The algorithm relies on reshaping...

A constructive arbitrary-degree Kronecker product decomposition of matrices

We propose a constructive algorithm, called the tensor-based Kronecker product (KP) singular value decomposition (TKPSVD), that decomposes an arbitrary real matrix A into a finite sum of KP terms with an arbitrary number of d factors, namely A = ∑R j=1 σj A dj ⊗ · · · ⊗A1j . The algorithm relies on reshaping and permuting the original matrix into a d-way tensor, after which its tensor-train ran...

Shifted Kronecker Product Systems

Abstract. A fast method for solving a linear system of the form (A(p) ⊗ · · · ⊗ A(1) − λI)x = b is given where each A(i) is an ni-by-ni matrix. The first step is to convert the problem to triangular form (T (p) ⊗ · · · ⊗ T (1) − λI)y = c by computing the (complex) Schur decompositions of the A(i). This is followed by a recursive back-substitution process that fully exploits the Kronecker struct...

Transformation of the Kronecker Product

Kronecker Decomposition for Image Classification