Solving structured linear systems with large displacement rank

Solving structured linear systems with large displacement rank

Linear systems with structures such as Toeplitz, Vandermonde or Cauchy-likeness can be solved in O (̃α2n) operations, where n is the matrix size, α is its displacement rank, and O ̃ denotes the omission of logarithmic factors. We show that for such matrices, this cost can be reduced to O (̃αω−1n), where ω is a feasible exponent for matrix multiplication over the base field. The best known estimate...

Dynamical systems method for solving linear finite-rank operator equations

A version of the dynamical systems method (DSM) for solving ill-conditioned linear algebraic systems is studied. An a priori and an a posteriori stopping rules are justified. An iterative scheme is constructed for solving ill-conditioned linear algebraic systems.

Superfast Solution of Linear Equations with Low Displacement Rank

A METHOD FOR SOLVING FUZZY LINEAR SYSTEMS

In this paper we present a method for solving fuzzy linear systemsby two crisp linear systems. Also necessary and sufficient conditions for existenceof solution are given. Some numerical examples illustrate the efficiencyof the method.

Algorithms for Structured Linear Systems Solving and Their Implementation

Œere exists a vast literature dedicated to algorithms for structured matrices, but relatively few descriptions of actual implementations and their practical performance in symbolic computation. In this paper, we consider the problem of solving Cauchy-like systems, and its application to mosaic Toeplitz systems, in two contexts: €rst in the unit cost model (which is a good model for computations...