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Performance analysis of Krylov iterative solvers using Ritz values Irina Craciun

Summary: Performance analysis of Krylov iterative solvers using Ritz values
Irina Craciun
Advisor: Dr. Burak Aksoylu
Center for Computation and Technology
Louisiana State University - Baton Rouge
1. Introduction
The problem of solving linear systems has become a crucial issue for scientific computing during
the past 50 years. A majority of problems in physics, astrophysics, computational fluid dynamics,
chemistry, engineering etc. reduce to solving a differential or integral equation, which in turn,
after discretisation and linearisation, reduce to a linear system of the form Ax = b. Coming from
real-life problems, the matrices are usually non-normal and very large - often reaching orders of
millions. For such large matrices, any linear solver fails because of computational errors.
On the positive side, they are also often sparse matrices (contain very few non-zero entries), which
makes the computation of matrix-vector products a very easy, non-costing task. This is why we
use iterative methods to solve large sparse linear systems: iterative methods generate successive
approximations of the solution, such that each approximation is computed from the previous one
through a series of matrix-vector products.
Currently there is no "perfect" iterative method; each known iterative method has been proved
efficient for some particular types of matrices and inefficient for others, each having many circum-


Source: Allen, Gabrielle - Department of Computer Science, Louisiana State University


Collections: Computer Technologies and Information Sciences