A generalization of the linear fractional integral equation u(t) = u0 + ∂−αAu(t), 1 < α < 2, which is written as a Volterra matrix–valued equation when applied as a pixel–by–pixel technique, has been proposed for image denoising (restoration, smoothing,...). Since the fractional integral equation interpolates a linear parabolic equation and a hyperbolic equation, the solution enjoys intermediat...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

consider the linear system ax=b where the coefficient matrix a is an m-matrix. in the present work, it is proved that the rate of convergence of the gauss-seidel method is faster than the mixed-type splitting and aor (sor) iterative methods for solving m-matrix linear systems. furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a precondition...

In this paper, a new algorithm for Sparse Component Analysis (SCA) or atomic decomposition on over-complete dictionaries is presented. The algorithm is essentially a method for obtaining sufficiently sparse solutions of underdetermined systems of linear equations. The solution obtained by the proposed algorithm is compared with the minimum `-norm solution achieved by Linear Programming (LP). It...

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...

In this paper, a fast algorithm for overcomplete sparse decomposition, called SL0, is proposed. The algorithm is essentially a method for obtaining sparse solutions of underdetermined systems of linear equations, and its applications include underdetermined Sparse Component Analysis (SCA), atomic decomposition on overcomplete dictionaries, compressed sensing, and decoding real field codes. Cont...

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...

Many linear algebra problems over the ring ZZN of integers modulo N can be solved by transforming via elementary row operations an n ⇥ m input matrix A to Howell form H. The nonzero rows of H give a canonical set of generators for the submodule of (ZZN ) m generated by the rows of A. In this paper we present an algorithm to recover H together with an invertible transformation matrix P which sat...

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.