Abstract In this article, quadrature rules for the efficient computation of stiffness matrix fractional Laplacian in three dimensions are presented. These based on Duffy transformation, which is a common tool singularity removal. Here, transformation adapted to needs dimensions. The integrals resulting from regular over less-dimensional domains. We present bounds number Gauss points guarantee e...

Approximations of matrix-valued functions of the form WT f(A)W , where A ∈ Rm×m is symmetric, W ∈ Rm×k , with m large and k m, has orthonormal columns, and f is a function, can be computed by applying a few steps of the symmetric block Lanczos method to A with initial block-vector W ∈ Rm×k . Golub and Meurant have shown that the approximants obtained in this manner may be considered block Gauss...

In this note, we study a concatenation of quasi-Monte Carlo and plain Monte rules for high-dimensional numerical integration in weighted function spaces. particular, consider approximating the integral periodic functions defined over $s$-dimensional unit cube by using rank-1 lattice point sets only first $d\, (<s)$ coordinates random points remaining $s-d$ coordinates. We prove that, exploiting...