Related papers: Nearly Pentadiagonal Linear Systems
Linear algebraic primitives are at the core of many modern algorithms in engineering, science, and machine learning. Hence, accelerating these primitives with novel computing hardware would have tremendous economic impact. Quantum computing…
A simple yet efficient computational algorithm for computing the continuous optimal experimental design for linear models is proposed. An alternative proof the monotonic convergence for $D$-optimal criterion on continuous design spaces are…
Basing on a modification of the "Dichotomy Algorithm" (Terekhov, 2010), we propose a parallel procedure for solving tridiagonal systems of equations with Toeplitz matrices. Taking the structure of the Toeplitz matrices, we may substantially…
We discuss the parallelization of algorithms for solving polynomial systems symbolically by way of triangular decomposition. Algorithms for solving polynomial systems combine low-level routines for performing arithmetic operations on…
Solving a quadratic nonlinear system of equations (QNSE) is a fundamental, but important, task in nonlinear science. We propose an efficient quantum algorithm for solving $n$-dimensional QNSE. Our algorithm embeds QNSE into a…
We present a numerical algorithm for finding real non-negative solutions to polynomial equations. Our methods are based on the expectation maximization and iterative proportional fitting algorithms, which are used in statistics to find…
Mixed packing and covering problems are problems that can be formulated as linear programs using only non-negative coefficients. Examples include multicommodity network flow, the Held-Karp lower bound on TSP, fractional relaxations of set…
PENLAB is an open source software package for nonlinear optimization, linear and nonlinear semidefinite optimization and any combination of these. It is written entirely in MATLAB. PENLAB is a young brother of our code PENNON \cite{pennon}…
Recent work in theoretical computer science and scientific computing has focused on nearly-linear-time algorithms for solving systems of linear equations. While introducing several novel theoretical perspectives, this work has yet to lead…
In this paper we consider linear systems of $\mathbb{P}^2$ with all but one of the base points of multiplicity 5. We give an explicit way to evaluate the dimensions of such systems.
In this paper we present a methodology for data accesses when solving batches of Tridiagonal and Pentadiagonal matrices that all share the same left-hand-side (LHS) matrix. The intended application is to the numerical solution of Partial…
An algorithm is presented for the computation of the topology of a non-reduced space curve defined as the intersection of two implicit algebraic surfaces. It computes a Piecewise Linear Structure (PLS) isotopic to the original space curve.…
We give an efficient algorithm for finding sparse approximate solutions to linear systems of equations with nonnegative coefficients. Unlike most known results for sparse recovery, we do not require {\em any} assumption on the matrix other…
We consider polynomial systems of Prony type, appearing in many areas of mathematics. Their robust numerical solution is considered to be difficult, especially in "near-colliding" situations. We consider a case when the structure of the…
In this work, we present a multiscale approach for the reliable coarse-scale approximation of spatial network models represented by a linear system of equations with respect to the nodes of a graph. The method is based on the ideas of the…
Projection algorithms are well known for their simplicity and flexibility in solving feasibility problems. They are particularly important in practice due to minimal requirements for software implementation and maintenance. In this work, we…
We investigate the conditions under which systems of two differential eigenvalue equations are quasi exactly solvable. These systems reveal a rich set of algebraic structures. Some of them are explicitely described. An exemple of quasi…
The results of computational experiments with ABS algorithms for overdetermined linear systems are reported.
This paper investigates analytical approximate solutions for a system of multipantograph delay differential equations using the residual power series method (RPSM), which obtains a Taylor expansion of the solutions and produces the exact…
This article introduces a general purpose framework and software to approximate partial differential equations (PDEs). The sparsity patterns of finite element discretized operators is identified automatically using the tools from…