This paper is concerned with factor left prime factorization problems for multivariate polynomial matrices without full row rank. We propose a necessary and sufficient condition the existence of factorizations class matrices, then design an algorithm to compute all if they exist. implement on computer algebra system Maple, two examples are given illustrate effectiveness algorithm. The results p...

In this paper we propose a method for the approximation of high-dimensional functions over finite intervals with respect to complete orthonormal systems polynomials. An important tool is multivariate classical analysis variance (ANOVA) decomposition. For low-dimensional structure, i.e., low superposition dimension, are able achieve reconstruction from scattered data and simultaneously understan...

The equivalence of systems is a crucial concept in multidimensional systems. Smith normal forms multivariate polynomial matrices play important roles the theory matrices. In this paper, we mainly study unimodular some special kinds and obtain tractable criteria under which such are equivalent to their forms. We propose an algorithm for reducing nD present example illustrate availability algorit...