In geophysical applications direct current (DC) resistivity surveys are collected by injecting current and recording voltage potentials over a field site of interest. These data sets can provide valuable non-invasive images of the sub-surface. The optimization problem that arrises in producing these images requires multiple solves of a linear system with numerous right hand sides (RHSs). Due to...

Block Toeplitz matrices are a special class of that exhibit reduced memory requirements and complexity matrix-vector multiplications. We herein present an efficient computational approach to solve sequence block systems arising from system with multiple right-hand sides. Two different numerical schemes implemented for the solution based on global variants generalized minimal residual (GMRES) me...

In a wide number of applications in computational science and engineering the solution of large linear systems of equations with several right-hand sides given at once is required. Direct methods based on Gaussian elimination are known to be especially appealing in that setting. Nevertheless when the dimension of the problem is very large, preconditioned block Krylov space solvers are often con...

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 dened. It is p...

We consider an extension of a linear model studied by Gale, Kuhn and Tucker (GKT) for an optimization problem with multiple criteria and multiple right-hand sides (resources), in which the constraints are nonlinear convex functions. We establish a strong duality result for the above model, of which the GKT result is a special case.

Global and block Krylov subspace methods are efficient iterative solvers for large sparse linear systems with multiple right-hand sides. However, global or Lanczos-type often exhibit oscillations in the residual norms may have a gap relating to loss of attainable accuracy approximations. Conventional smoothing schemes suppress these but cannot improve accuracy, whereas recent scheme enables imp...