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Fast Fourier transform algorithms are an arsenal of effective tools for solving various problems of analysis and high-speed processing of signals of various natures. Almost all of these algorithms are designed to process sequences of…
Polyhedral Omega is a new algorithm for solving linear Diophantine systems (LDS), i.e., for computing a multivariate rational function representation of the set of all non-negative integer solutions to a system of linear equations and…
The object of the present paper is to extend the third-order iterative method for solving nonlinear equations into systems of nonlinear equations. Since our motive is to develop the method which improve the order of convergence of Newton's…
New solution method for the systems of linear equations in commutative integral domains is proposed. Its complexity is the same that the complexity of the matrix multiplication.
Large sparse symmetric linear systems appear in several branches of science and engineering thanks to the widespread use of the finite element method (FEM). The fastest sparse linear solvers available implement hybrid iterative methods.…
Recent results by Harrow et. al. and by Ta-Shma, suggest that quantum computers may have an exponential advantage in solving a wealth of linear algebraic problems, over classical algorithms. Building on the quantum intuition of these…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
While quantum computing provides an exponential advantage in solving system of linear equations, there is little work to solve system of nonlinear equations with quantum computing. We propose quantum Newton's method (QNM) for solving…
Recent work in deep learning has opened new possibilities for solving classical algorithmic tasks using end-to-end learned models. In this work, we investigate the fundamental task of solving linear systems, particularly those that are…
In numerical linear algebra, considerable effort has been devoted to obtaining faster algorithms for linear systems whose underlying matrices exhibit structural properties. A prominent success story is the method of generalized nested…
Dantzig's vertex pivot simplex method has been published for more than seven decades. Amazingly, it remains one of the most efficient methods to solve linear programming (LP) problem after numerous efforts trying to find some better…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
We propose a new algorithm to the problem of polygonal curve approximation based on a multiresolution approach. This algorithm is suboptimal but still maintains some optimality between successive levels of resolution using dynamic…
We propose a new approach to the combinatorial interpretations of linearization coefficient problem of orthogonal polynomials. We first establish a difference system and then solve it combinatorially and analytically using the method of…
This paper offers a matrix-free first-order numerical method to solve large-scale conic optimization problems. Solving systems of linear equations pose the most computationally challenging part in both first-order and second-order numerical…
The work is devoted to the development of numerical methods for computing "formal solutions" of interval systems of linear algebraic equations. These solutions are found in Kaucher interval arithmetic, which extends and completes the…
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
A new iterative technique is presented for solving of initial value problem for certain classes of multidimensional linear and nonlinear partial differential equations. Proposed iterative scheme does not require any discretization,…
We propose in this paper a Proper Generalized Decomposition (PGD) solver for reduced-order modeling of linear elastodynamic problems. It primarily focuses on enhancing the computational efficiency of a previously introduced PGD solver based…
In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences, and we find the number of distinct solutions. Many examples of solving congruences are given.