A new optimized iterative method for solving $M$-matrix linear systems

Alireza Fakharzadeh Jahromi; Nafiseh Nasseri Shams

Displaying similar documents to “A new optimized iterative method for solving $M$ -matrix linear systems”

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

Kocurek, Martin

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This article presents a simple method for bounding a solution of a system of linear equations $A x = b$ 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.

A dual-parameter double-step splitting iteration method for solving complex symmetric linear equations

Beibei Li, Jingjing Cui, Zhengge Huang, Xiaofeng Xie (2024)

Applications of Mathematics

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We multiply both sides of the complex symmetric linear system $A x = b$ by $1 - i ω$ to obtain a new equivalent linear system, then a dual-parameter double-step splitting (DDSS) method is established for solving the new linear system. In addition, we present an upper bound for the spectral radius of iteration matrix of the DDSS method and obtain its quasi-optimal parameter. Theoretical analyses demonstrate that the new method is convergent when some conditions are satisfied. Some tested examples are...

On the subspace projected approximate matrix method

Jan Brandts, Ricardo Reis da Silva (2015)

Applications of Mathematics

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We provide a comparative study of the Subspace Projected Approximate Matrix method, abbreviated SPAM, which is a fairly recent iterative method of computing a few eigenvalues of a Hermitian matrix $A$ . It falls in the category of inner-outer iteration methods and aims to reduce the costs of matrix-vector products with $A$ within its inner iteration. This is done by choosing an approximation $A_{0}$ of $A$ , and then, based on both $A$ and $A_{0}$ , to define a sequence ${(A_{k})}_{k = 0}^{n}$ of matrices that increasingly better...

The new iteration methods for solving absolute value equations

Rashid Ali, Kejia Pan (2023)

Applications of Mathematics

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Many problems in operations research, management science, and engineering fields lead to the solution of absolute value equations. In this study, we propose two new iteration methods for solving absolute value equations $A x - | x | = b$ , where $A \in ℝ^{n \times n}$ is an $M$ -matrix or strictly diagonally dominant matrix, $b \in ℝ^{n}$ and $x \in ℝ^{n}$ is an unknown solution vector. Furthermore, we discuss the convergence of the proposed two methods under suitable assumptions. Numerical experiments are given to verify the feasibility, robustness...

Nonsingularity, positive definiteness, and positive invertibility under fixed-point data rounding

Jiří Rohn (2007)

Applications of Mathematics

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For a real square matrix $A$ and an integer $d \geq 0$ , let $A_{(d)}$ denote the matrix formed from $A$ by rounding off all its coefficients to $d$ decimal places. The main problem handled in this paper is the following: assuming that $A_{(d)}$ has some property, under what additional condition(s) can we be sure that the original matrix $A$ possesses the same property? Three properties are investigated: nonsingularity, positive definiteness, and positive invertibility. In all three cases it is shown that there exists...

Circulant matrices with orthogonal rows and off-diagonal entries of absolute value $1$

Daniel Uzcátegui Contreras, Dardo Goyeneche, Ondřej Turek, Zuzana Václavíková (2021)

Communications in Mathematics

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It is known that a real symmetric circulant matrix with diagonal entries $d \geq 0$ , off-diagonal entries $\pm 1$ and orthogonal rows exists only of order $2 d + 2$ (and trivially of order $1$ ) [Turek and Goyeneche 2019]. In this paper we consider a complex Hermitian analogy of those matrices. That is, we study the existence and construction of Hermitian circulant matrices having orthogonal rows, diagonal entries $d \geq 0$ and any complex entries of absolute value $1$ off the diagonal. As a particular case, we consider...

Investigating generalized quaternions with dual-generalized complex numbers

Nurten Gürses, Gülsüm Yeliz Şentürk, Salim Yüce (2023)

Mathematica Bohemica

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We aim to introduce generalized quaternions with dual-generalized complex number coefficients for all real values $α$ , $β$ and $𝔭$ . Furthermore, the algebraic structures, properties and matrix forms are expressed as generalized quaternions and dual-generalized complex numbers. Finally, based on their matrix representations, the multiplication of these quaternions is restated and numerical examples are given.

Hermitian operators on $H_{E}^{\infty}$ and $S_{}^{\infty}$

James Jamison (2013)

Colloquium Mathematicae

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A complete characterization of bounded and unbounded norm hermitian operators on $H_{E}^{\infty}$ is given for the case when E is a complex Banach space with trivial multiplier algebra. As a consequence, the bi-circular projections on $H_{E}^{\infty}$ are determined. We also characterize a subclass of hermitian operators on $S_{}^{\infty}$ for a complex Hilbert space.

On the matrix negative Pell equation

Aleksander Grytczuk, Izabela Kurzydło (2009)

Discussiones Mathematicae - General Algebra and Applications

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Let N be a set of natural numbers and Z be a set of integers. Let M₂(Z) denotes the set of all 2x2 matrices with integer entries. We give necessary and suficient conditions for solvability of the matrix negative Pell equation (P) X² - dY² = -I with d ∈ N for nonsingular X,Y belonging to M₂(Z) and his generalization (Pn) $\sum_{i = 1}^{n} X ₂_{i} - d \sum_{i = 1}^{n} Y ²_{i} = - I$ with d ∈ N for nonsingular $X_{i}, Y_{i} \in M ₂ (Z)$ , i=1,...,n.

Ground states of supersymmetric matrix models

Gian Michele Graf (1998-1999)

Séminaire Équations aux dérivées partielles

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We consider supersymmetric matrix Hamiltonians. The existence of a zero-energy bound state, in particular for the $d = 9$ model, is of interest in M-theory. While we do not quite prove its existence, we show that the decay at infinity such a state would have is compatible with normalizability (and hence existence) in $d = 9$ . Moreover, it would be unique. Other values of $d$ , where the situation is somewhat different, shall also be addressed. The analysis is based on a Born-Oppenheimer approximation....

Displaying similar documents to “A new optimized iterative method for solving M -matrix linear systems”

Displaying similar documents to “A new optimized iterative method for solving $M$ -matrix linear systems”