Computing error bounds in solving linear systems

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.

Defuzzification method for solving fuzzy linear systems

Lurupa - Rigorous Error Bounds in Linear Programming

Rigorous Error Bounds in Linear Programming Christian Keil Hamburg University of Te hnology, Institute for Reliable Computing .keil tu-harburg.de Abstra t. Linear Programming has numerous appli ations. Re ently it has been shown that many real world problems exhibit numeri al di ulties due to illonditioning. This paper des ribes Lurupa, a software pa kage for omputing rigorous bounds for the op...

Efficient Parallel Computing for Solving Linear Systems of Equations

Linear systems of equations are common throughout the disciplines of science. The conjugate gradient method is a common iterative method used to solve systems with symmetric positive definite system matrices. With a matrix-free implementation, the method is optimal with respect to both memory usage and performance, and we are able to solve problems that are much too large for single processor c...

On the Complexity of Computing Error Bounds

We consider the cost of estimating an error bound for the computed solution of a system of linear equations, i.e. estimating the norm of a matrix inverse. Under some technical assumptions we show that computing even a coarse error bound for the solution of a triangular system of equations costs at least as much as testing whether the product of two matrices is zero. The complexity of the latter...