Related papers: Effective Matrix Methods in Commutative Domains
From the matrix point of view, we use the recursion to discuss four combinatorial numbers in terms of the integer lattice paths, this is different from Andr\'a's method (Andra). We give four tables and matrices, and their relations, and…
A general framework based on Gaussian models and a MAP-EM algorithm is introduced in this paper for solving matrix/table completion problems. The numerical experiments with the standard and challenging movie ratings data show that the…
In this paper we propose an idea of constructing a macro--scale matrix system given a micro--scale matrix linear system. Then the macro--scale system is solved at cheaper computing costs. The method uses the idea of the generalized…
Discretizations of infinite-dimensional variational inequalities lead to linear and nonlinear complementarity problems with many degrees of freedom. To solve these problems in a parallel computing environment, we propose two active-set…
In this paper we outline a Matrix Ansatz approach to some problems of combinatorial enumeration. The idea is that many interesting quantities can be expressed in terms of products of matrices, where the matrices obey certain relations. We…
We assess the situation of our elementary Linear Algebra classes in the US holistically and through personal history recollections. Possible remedies for our elementary Linear Algebra's teaching problems are discussed and a change from…
We present a novel algebraic combinatorial view on low-rank matrix completion based on studying relations between a few entries with tools from algebraic geometry and matroid theory. The intrinsic locality of the approach allows for the…
In this article, we establish a class of new accelerated modulus-based iteration methods for solving the linear complementarity problem. When the system matrix is an $H_+$-matrix, we present appropriate criteria for the convergence…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
The multiplicative and additive compounds of a matrix play an important role in several fields of mathematics including geometry, multi-linear algebra, combinatorics, and the analysis of nonlinear time-varying dynamical systems. There is a…
Using exhaustion method and finite differences a new method to solve system of partial differential equations and is presented. This method allows design algorithm to solve linear and nonlinear systems in irregular domains. Applying this…
In this paper we focus on the solution of shifted quasiseparable systems and of more general parameter dependent matrix equations with quasiseparable representations. We propose an efficient algorithm exploiting the invariance of the…
We present certain techniques to find completely positive maps between matrix algebras that take prescribed values on given data. To this aim we describe a semidefinite programming approach and another convex minimization method supported…
The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…
Matrices can be augmented by adding additional columns such that a partitioning of the matrix in blocks of rows defines mutually orthogonal subspaces. This augmented system can then be solved efficiently by a sum of projections onto these…
To numerically solve a generic elliptic equation on two-dimensional domains with rectangular Cartesian grids, we propose a cut-cell geometric multigrid method that features (1) general algorithmic steps that apply to two-dimensional…
In this work we present a new approach for the implementation of operational Tau method for the solutions of linear differential and integral equations. In our approach we use the three terms relation of an orthogonal polynomial basis to…
In this paper we introduce a generic model for multiplicative algorithms which is suitable for the MapReduce parallel programming paradigm. We implement three typical machine learning algorithms to demonstrate how similarity comparison,…
We consider the solution of systems of linear algebraic equations (SLAEs) with an ill-conditioned or degenerate exact matrix and an approximate right-hand side. An approach to solving such a problem is proposed and justified, which makes it…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.