Kronecker descriptors are an efficient option to store the underlying Markov chain of a model in a structured and compact fashion. The basis of classical numerical solutions for Kronecker descriptors represented models is the VectorDescriptor Product (VDP). The Shuffle algorithm is the most popular VDP method to handle generalized descriptors, i.e., descriptors with functional elements. Recentl...

We describe an interface and an implementation for performing Kronecker product actions on NVIDIA GPUs for multiple small 2-D matrices and 3-D arrays processed in parallel as a batch. This method is suited to cases where the Kronecker product component matrices are identical but the operands in a matrix-free application vary in the batch. Any batched GEMM (General Matrix Multiply) implementatio...

Kronecker coefficients are tensor product multiplicities for the irreducible representations of the symmetric group. In this paper, we identify directions in the parameter space for tensor products along which these multiplicities are monotone convergent, generalizing a classical result of Murnaghan.

Regularization operators that penalize derivatives are approximated by Kronecker products. This allows direct regularization of multidimensional first-kind linear integral equations with separable kernels. An example of image deblurring is presented.

Some near-regular mechanical systems involve global deviations from their corresponding regular system. Despite extensive research on vibration analysis (eigensolution) of regular and local near-regular mechanical systems, the literature on vibration analysis of global near-regular mechanical systems is scant. In this paper, a method for vibration analysis of such systems was developed using Kr...

We saw in Lecture 3 how to efficiently multiply integers, and, using Kronecker substitution, how to efficiently multiply polynomials with integer coefficients. This gives us what we need to multiply elements in finite fields, provided that we have a way to reduce the result to our standard representations of Fp ' Z/pZ and Fq ' Fp[x]/(f), using integers in [0, p− 1] and polynomials of degree les...