A Non-Iterative Procedure for Sparse Solutions to Linear Equations with Bandlimited Rows

Preconditioned Generalized Minimal Residual Method for Solving Fractional Advection-Diffusion Equation

Introduction Fractional differential equations (FDEs)  have  attracted much attention and have been widely used in the fields of finance, physics, image processing, and biology, etc. It is not always possible to find an analytical solution for such equations. The approximate solution or numerical scheme  may be a good approach, particularly, the schemes in numerical linear algebra for solving ...

Summary of SuperLU

1 Overview of the Package SuperLU is a general-purpose library for the direct solution of large, sparse systems of linear equations on high performance machines. It is especially targeted for non-symmetric, non-definite systems. The library routines perform an LU factorization with numerical pivoting and triangular solutions through forward and back substitutions. The factorization can be appli...

New family of Two-Parameters Iterative Methods for Non-Linear Equations with Fourth-Order Convergence

Location of Non-Zeros in Sparse Solutions of Underdetermined Linear Systems of Equations

The problem of computing sparse (mostly zero) or sparsifiable (by linear transformation) solutions to greatly underdetermined linear systems of equations has applications in compressed sensing. The locations of the nonzero elements in the solution is a much smaller set of variables than the solution itself. We present explicit equations for the relatively few variables that determine these nonz...

A Non-Iterative Procedure for Computing Sparse and Sparsifiable Solutions to Slightly Underdetermined Linear Systems of Equations

The problem of computing sparse (mostly zero) solutions to underdetermined linear systems of equations has received much attention recently, due to its applications to compressed sensing. Under mild assumptions, the sparsest solution has minimum-L1norm, and can be computed using linear programming. In some applications (valid deconvolution, singular linear transformations), the linear system is...