The global Golub-Kahan method and Gauss quadrature for tensor function approximation

This paper is concerned with Krylov subspace methods based on the tensor t-product for  computing certain quantities associated with generalized third-order tensor functions. We use the tensor t-product and define the tensor global Golub-Kahan bidiagonalization process for approximating tensor functions. Pairs of Gauss and Gauss-Radau quadrature rules are applied to determine the desired quantities with error bounds. An application to the computation of the tensor nuclear norm is presented and illustrates the effectiveness of the proposed methods.