Related papers: A New Operator and Method for Solving Interval Lin…
Linear equations play a pivotal role in many areas of science and engineering, making efficient solutions to linear systems highly desirable. The development of quantum algorithms for solving linear systems has been a significant…
This paper is devoted to a new approach of the arithmetic of intervals. We present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any…
For multi-block alternating direction method of multipliers(ADMM), where the objective function can be decomposed into multiple block components, we show that with block symmetric Gauss-Seidel iteration, the algorithm will converge quickly.…
Consider the classical problem of solving a general linear system of equations $Ax=b$. It is well known that the (successively over relaxed) Gauss-Seidel scheme and many of its variants may not converge when $A$ is neither diagonally…
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new classes of bispectral operators.
The solution of systems of non-autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in…
The improvement in observational facilities requires refining the modelling of the geometrical structures of astrophysical objects. Nevertheless, for complex problems such as line overlap in molecules showing hyperfine structure, a detailed…
A nonlinear equation in a Banach space is written as a linear equation with a linear operator depending on the unknown solution. This method, which we call a global linearization method, differs essentially from the local linearization…
This paper offers a contemporary and comprehensive perspective on the classical algorithms utilized for the solution of minimum-time problem for linear systems (MTPLS). The use of unified notations supported by visual geometric…
In this paper we present the set of intervals as a normed vector space. We define also a four-dimensional associative algebra whose product gives the product of intervals in any cases. This approach allows to give a notion of divisibility…
The work is devoted to the construction of a new interval arithmetic which would combine algorithmic efficiency and high quality estimation of the ranges of expressions.
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization, $\ell_1$ norm regularized optimization, and $\ell_0$ norm regularized…
In this paper, we study how the D-iteration algorithm can be applied to numerically solve the differential equations such as heat equation in 2D or 3D. The method can be applied on the class of problems that can be addressed by the…
We propose a new algorithm to solve sparse linear systems of equations over the integers. This algorithm is based on a $p$-adic lifting technique combined with the use of block matrices with structured blocks. It achieves a sub-cubic…
In this paper, we consider the solution of ill-conditioned systems of linear algebraic equations that can be determined imprecisely. To improve the stability of the solution process, we "immerse" the original imprecise linear system in an…
We use linear algebraic methods to obtain general results about linear operators on a space of polynomials that we apply to the operators associated with a polynomial sequence by the monomiality property. We show that all such operators are…
The multigrid algorithm is an efficient numerical method for solving a variety of elliptic partial differential equations (PDEs). The method damps errors at progressively finer grid scales, resulting in faster convergence compared to…
We consider a wide class of the discrete optimization problems with interval objective function. We give a generalization of the greedy algorithm for the problems. Using the algorithm, we obtain the set of all possible greedy solutions and…
We develop an operator approach to the integration of linear differential equations based on intertwining relations between differential operators. Conditions for the existence of intertwining operators are obtained, and it is shown that,…
In this work, we investigate the interval generalized Sylvester matrix equation ${\bf{A}}X{\bf{B}}+{\bf{C}}X{\bf{D}}={\bf{F}}$ and develop some techniques for obtaining outer estimations for the so-called united solution set of this…