The repeated trapezoidal method was considered by P. Eggermont for the numerical solution of weakly singular Volterra integral equations of the first kind with exactly given right-hand sides ([7]). In the present paper we consider the regularizing properties of this method for perturbed right-hand sides. Finally, numerical results are presented.

An application of the Generalized Minimal Residual (GMRES) algorithm to the solution of sequentially multiple nearby systems of equations through the reuse of Krylov subspaces is presented. The main focus is on the case when only the right-hand side vector changes. However, the case in which both the matrix and the right-hand side change is also addressed. Applications of these formulations inc...

Many statistical applications require the solution of a symmetric positive definite covariance matrix, sometimes with a large number of right-hand sides of a statistical independence nature. With preconditioning, the preconditioned matrix has almost all the eigenvalues clustered within a narrow range, except for a few extreme eigenvalues deviating from the range rapidly. We derive a deflated ve...

in this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s a_jx_jb_j = e$. this method is based on the global least squares (gl-lsqr) method for solving the linear system of equations with the multiple right hand sides. for applying the gl-lsqr algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. it is ...

A new method for solving algebraic equation systems common in cryptanalysis is proposed. Our method differs from the others in that the equations are not represented as multivariate polynomials, but as a system of Multiple Right Hand Sides linear equations. The method was tested on scaled versions of the AES. The results overcome significantly what was previously achieved with Gröbner Basis rel...

We investigate a new storage format for unstructured sparse matrices, based on the space filling Hilbert curve. Numerical tests with matrix-vector multiplication show the potential of the fractal storage format (FS) in comparison to the traditional compressed row storage format (CRS). The FS format outperforms the CRS format by up to 50% for matrix-vector multiplications with multiple right han...

Computing quark propagators in lattice QCD is equivalent to solving large, sparse linear systems with multiple right-hand sides. Block algorithms attempt to accelerate the convergence of iterative Krylov-subspace methods by solving the multiple systems simultaneously. This paper compares a block generalisation of the quasi-minimal residual method (QMR), Block Conjugate Gradient on the normal eq...