minimal pseudoinverse matrix methodThe problem of solving systems of linear equations with an ill-conditioned or degenerate exact matrix and an approximate right-hand side is considered. A scheme for solving such a problem is proposed and justified, which allows improving the conditionality of the ...
MATLAB solves such linear equations without computing the inverse of the matrix. The two division symbols, slash, /, and backslash, \, are used for the two situations where the unknown matrix appears on the left or right of the coefficient matrix. ...
Recently, a matrix exponential based algorithm for solving a symmetric positive de nite (SPD) system of linear equations (the EXP algorithm) has been proposed [14]. The EXP algorithm is highly parallelizable and therefore provides greater margin of speed up through parallelization than the existing...
Efficient continuation Newton-like method for solving systems of non-linear equations In this paper, we present a new Newton-like method for finding a zero of a vector function, permitting that the Jacobian is singular in some points. Thus, ... LX Wang - 《Applied Mathematics & Computation》...
Separable nonlinear equations have the form where the matrix and the vector are continuously differentiable functions of and . We assume that and has full rank. We present a numerical method to compute the solution for fully determined systems ( ) and co
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Besides the Bayesian formulation explained below, there are other approaches for deriving the linear inverse operators which will be described, such as minimization of expected error and generalized Wiener filtering. Details are given in [12]. Bayesian methods can also be used to estimate a probabili...
This paper presents an optimization technique for solving linear system problems with more number of equations than unknown variables using Euclidean Space theory and least squares method. In view to automating the technique, we developed software in FORTRAN code for a generalized case. The technique ...
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by a set of randomly sampled data point clouds that are as...
From the results of numerical experiments given in the last section, we can conclude that the proposed method is effective in solving linear peridynamic equations in terms of accuracy, computational efficiency, and stability. Based on this approach, we further explore the performance of the peridynami...