This paper is focused on di1erent methods and algorithms for solving tridiagonal block Toeplitz systems of linear equations. We consider the El-Sayed method (Ph.D. Thesis, 1996) for such systems and propose several modi9cations that lead to di1erent algorithms, which we discuss in detail. Our algorithms are then compared with some classical techniques as far as implementation time is concerned,...

It appears that large scale calculations in particle physics often require to solve systems of linear equations with rational number coefficients exactly. If classical Gaussian elimination is applied to a dense system, the time needed to solve such a system grows exponentially in the size of the system. In this tutorial paper, we present a standard technique from computer algebra that avoids th...

Some of the most widely used algorithms for two-point boundary value ODEs, namely nite diierence and collocation methods and standard multiple shooting, proceed by setting up and solving a structured system of linear equations. It is well known that the linear system can be set up eeciently in parallel; we show here that a structured orthogonal factorization technique can be used to solve this ...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...

Solving large sparse systems of linear equations is at the core of many problems in engineering and scienti c computing. It has long been a challenge to develop parallel formulations of sparse direct solvers due to several di erent complex steps involved in the process. In this paper, we describe one of the rst e cient, practical, and robust parallel solvers for sparse symmetric positive de nit...

Systems of linear equations arise at the heart of many scientific and engineering applications. Many of these linear systems are sparse; i.e., most of the elements in the coefficient matrix are zero. Direct methods based on matrix factorizations are sometimes needed to ensure accurate solutions. For example, accurate solution of sparse linear systems is needed in shift-invert Lanczos to compute...

The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear equations with sparse solutions. The speedup is achieved by projecting every iterate onto a weighted row of the linear system while maintaining the random r...

A new parallel approach for solving a pentadiagonal linear system is presented. The parallel partition method for this system and the TW parallel partition method on a chain of P processors are introduced and discussed. The result of this algorithm is a reduced pentadiagonal linear system of order P 2 compared with a system of order 2P 2 for the parallel partition method. More importantly the n...

The problem of solving a system of linear equations is equivalent to the computation of biorthogonal polynomials and to the bordering method which is a procedure for solving recursively a sequence of linear systems with increasing dimensions. In some cases, the biorthogonal polynomials can be computed recursively thus leading to procedures for solving linear systems. The particular cases of Han...

A new effective modification of the method which is described in [1] for solving of real symmetric circulant pentadiagonal systems of linear equations is proposed. We consider the case where the coefficient matrix is not diagonal dominant. This paper shows efficiency and stability of the presented method.