## Displaying similar documents to “Geometric convergence of iterative methods for variational inequalities with $M$-matrices and diagonal monotone operators”

### The use of basic iterative methods for bounding a solution of a system of linear equations with an M-matrix and positive right-hand side

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This article presents a simple method for bounding a solution of a system of linear equations $Ax=b$ with an M-matrix and positive right-hand side . Given a suitable approximation to an exact solution, the bounds are constructed by one step in a basic iterative method.

### Analysis of approximate solutions of coupled dynamical thermoelasticity and related problems

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...

### Nested matrices and inverse $M$-matrices

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 $LU$- and $QR$-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 $M$-matrices with symmetric, irreducible, tridiagonal inverses.

### A convergence analysis of SOR iterative methods for linear systems with weakH-matrices

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...

### A convergent nonlinear splitting via orthogonal projection

Aplikace matematiky

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We study the convergence of the iterations in a Hilbert space $V,{x}_{k+1}=W\left(P\right){x}_{k},W\left(P\right)z=w=T\left(Pw+\left(I-P\right)z\right)$, where $T$ maps $V$ into itself and $P$ is a linear projection operator. The iterations converge to the unique fixed point of $T$, if the operator $W\left(P\right)$ is continuous and the Lipschitz constant $∥\left(I-P\right)W\left(P\right)∥<1$. If an operator $W\left({P}_{1}\right)$ satisfies these assumptions and ${P}_{2}$ is an orthogonal projection such that ${P}_{1}{P}_{2}={P}_{2}{P}_{1}={P}_{1}$, then the operator $W\left({P}_{2}\right)$ is defined and continuous in $V$ and satisfies $∥\left(I-{P}_{2}\right)W\left({P}_{2}\right)∥\le ∥\left(I-{P}_{1}\right)W\left({P}_{1}\right)∥$.

### New modification of Maheshwari’s method with optimal eighth order convergence for solving nonlinear equations

Open Mathematics

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In this paper, we present a family of three-point with eight-order convergence methods for finding the simple roots of nonlinear equations by suitable approximations and weight function based on Maheshwari’s method. Per iteration this method requires three evaluations of the function and one evaluation of its first derivative. These class of methods have the efficiency index equal to [...] 814≈1.682${8}^{\frac{1}{4}}\approx 1.682$. We describe the analysis of the proposed methods along with numerical experiments including...

### On the statistical and σ-cores

Studia Mathematica

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In  and , the concepts of σ-core and statistical core of a bounded number sequence x have been introduced and also some inequalities which are analogues of Knopp’s core theorem have been proved. In this paper, we characterize the matrices of the class ${\left(S\cap m,{V}_{\sigma }\right)}_{reg}$ and determine necessary and sufficient conditions for a matrix A to satisfy σ-core(Ax) ⊆ st-core(x) for all x ∈ m.

Acta Arithmetica

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### Doubly stochastic matrices and the Bruhat order

Czechoslovak Mathematical Journal

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The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order $n$ which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, which we call the stochastic Bruhat order, for the larger class ${\Omega }_{n}$ of doubly stochastic matrices (convex hull of $n×n$ permutation matrices). An alternative description of this partial order is given. We define a class of special faces of ${\Omega }_{n}$ induced by permutation...

### On the Existence of Solutions for Abstract Nonlinear Operator Equations

Bollettino dell'Unione Matematica Italiana

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We provide a duality theory and existence results for a operator equation $\nabla T(x)=\nabla N(x)$ where $T$ is not necessarily a monotone operator. We use the abstract version of the so called dual variational method. The solution is obtained as a limit of a minimizng sequence whose existence and convergence is proved.

### A Short Proof of the Variational Principle for a ${ℤ}_{+}^{N}$ Action on a Compact Space

Publications mathématiques et informatique de Rennes

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