Keywords: Additive/multiplicative splitting iteration method Singular linear systems Hermitian matrix Semiconvergence a b s t r a c t In this paper, we investigate the additive, multiplicative and general splitting iteration methods for solving singular linear systems. When the coefficient matrix is Hermitian, the semiconvergence conditions are proposed, which generalize some results of Bai [Z....

We prove a removal lemma for systems of linear equations over finite fields: let X1, . . . , Xm be subsets of the finite field Fq and let A be a (k×m) matrix with coefficients in Fq and rank k; if the linear system Ax = b has o(q) solutions with xi ∈ Xi, then we can destroy all these solutions by deleting o(q) elements from each Xi. This extends a result of Green [Geometric and Functional Analy...

We present a development of Dodgson’s method for the solution to a system of linear equations (see [5]) using the determinants of the Sylvester’s (Determinants) Identity. We explicitly write down the algorithm for this developed method. Mathematics Subject Classification: Primary 05A19; Secondary 05A10

Notice that the left-hand side of the third equation is the sum of the left-hand sides of the first two. As a result, no solution to the system exists unless a + b = c. But if a + b = c, then any solution of the first two equations is also a solution of the third; and in any linear system involving more unknowns than equations, solutions, when they exist, are never unique. In the present case, ...

In this paper, updating algorithms for solving linear systems of equations are presented using a systolic array model. First, a parallel algorithm for computing the inverse of rank-one modiied matrix using the Sherman-Morrison formula is proposed. This algorithm is then extended to solving the updated systems of linear equations on a linear systolic array. Finally, the generalisation to the upd...

We present computational results using CORAL, a parallel, three-dimensional, nonlinear magnetostatic code based on a volume integral equation formulation. A key feature of CORAL is the ability to solve, in parallel, the large, dense systems of linear equations that are inherent in the use of integral equation methods. Using the Chameleon and PSLES libraries ensures portability and access to the...

This paper shows the complementary roles of mathematical and engineering points of view when dealing with truss analysis problems involving systems of linear equations and inequalities. After the compatibility condition and the mathematical structure of the general solution of a system of linear equations is discussed, the truss analysis problem is used to illustrate its mathematical and engine...

For the non-Hermitian and positive semidefinite systems of linear equations, we derive sufficient and necessary conditions for guaranteeing the unconditional convergence of the preconditioned Hermitian and skew-Hermitian splitting iteration methods. These result is specifically applied to linear systems of block tridiagonal form to obtain convergence conditions for the corresponding block varia...

In this paper we present an extension of the removal lemma to integer linear systems over abelian groups. We prove that, if the k– determinantal of an integer (k×m) matrix A is coprime with the order n of a group G and the number of solutions of the system Ax = b with x1 ∈ X1, . . . , xm ∈ Xm is o(n ), then we can eliminate o(n) elements in each set to remove all these solutions. algebraic remo...

This article proposes an optimal method for approximate answer of stochastic Ito-Voltrra integral equations, via rationalized Haar functions and their stochastic operational matrix of integration. Stochastic Ito-voltreea integral equation is reduced to a system of linear equations. This scheme is applied for some examples. The results show the efficiency and accuracy of the method.