this work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $ax = b$ and $xc = d$ with orthogonal constraint. by optimal correction approach, a general representation of the orthogonal solution is obtained. this method is tested on two examples to show that the optimal correction is eective and highly accurate.

the main purpose of this article is to present an approximate solution for the two-dimensional nonlinear volterra integral equations using legendre orthogonal polynomials. first, the two-dimensional shifted legendre orthogonal polynomials are defined and the properties of these polynomials are presented. the operational matrix of integration and the product operational matrix are introduced. th...

We study certain sequences of rational matrix-valued functions with poles outside the unit circle. These sequences are recursively constructed based on a sequence of complex numbers with norm less than one and a sequence of strictly contractive matrices. We present some basic facts on the rational matrix-valued functions belonging to such kind of sequences and we will see that the validity of s...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q = 0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relation...

nonnegative matrix factorization (nmf) is a common method in data mining that have been used in different applications as a dimension reduction, classification or clustering method. methods in alternating least square (als) approach usually used to solve this non-convex minimization problem.  at each step of als algorithms two convex least square problems should be solved, which causes high com...

Block Wavelet Transforms (BWTs) are orthogonal matrix transforms that can be obtained from orthogonal subband filter banks. They were initially generated to produce matrix transforms which may carry nice properties inheriting from wavelets, as alternatives to DCT and similar matrix transforms. Although the construction methodology of BWT is clear, the reverse operation was not researched. In ce...

This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.