Kocurek, Martin
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This article presents a simple method for bounding a solution of a system of linear equations with an M-matrix and positive right-hand side [1]. Given a suitable approximation to an exact solution, the bounds are constructed by one step in a basic iterative method.
Vaibhav Shekhar, Nachiketa Mishra, Debasisha Mishra (2022)
Applications of Mathematics
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Recently, Wang (2017) has introduced the -nonnegative double splitting using the notion of matrices that leave a cone invariant and studied its convergence theory by generalizing the corresponding results for the nonnegative double splitting by Song and Song (2011). However, the convergence theory for -weak regular and -nonnegative double splittings of type II is not yet studied. In this article, we first introduce this class of splittings and then discuss the convergence theory...
Jozef Kačur, Alexander Ženíšek (1986)
Aplikace matematiky
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The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems. First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution...
Jeffrey L. Stuart (2015)
Czechoslovak Mathematical Journal
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Given a sequence of real or complex numbers, we construct a sequence of nested, symmetric matrices. We determine the - and -factorizations, the determinant and the principal minors for such a matrix. When the sequence is real, positive and strictly increasing, the matrices are strictly positive, inverse -matrices with symmetric, irreducible, tridiagonal inverses.
Cheng-yi Zhang, Zichen Xue, Shuanghua Luo (2016)
Open Mathematics
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It is well known that SOR iterative methods are convergent for linear systems, whose coefficient matrices are strictly or irreducibly diagonally dominant matrices and strong H-matrices (whose comparison matrices are nonsingular M-matrices). However, the same can not be true in case of those iterative methods for linear systems with weak H-matrices (whose comparison matrices are singular M-matrices). This paper proposes some necessary and sufficient conditions such that SOR iterative...
Jan Mandel (1984)
Aplikace matematiky
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We study the convergence of the iterations in a Hilbert space , where maps into itself and is a linear projection operator. The iterations converge to the unique fixed point of , if the operator is continuous and the Lipschitz constant . If an operator satisfies these assumptions and is an orthogonal projection such that , then the operator is defined and continuous in and satisfies .