Iterative Methods for large linear systems of equations
The solution of linear systems of
equations by iterative methods is essential whenever the dimensions of the
problems are that direct methods cannot be applied, or when only a low
accuracy solution is needed.
The design of efficient iterative methods for problems with specific
characteristics, e.g., with a special sparsity structure, large condition
numbers, or sequences of linear systems which changed very little from one
another is still receiving a lot of interest.
Iterative methods for the solution
of linear systems of equations produce a sequence of approximate solutions.
In many applications it is desirable to be able to compute estimates of the norm
of the error in the approximate solutions generated and terminate the
iterations when the estimates are sufficiently small.
The research has focused on new iterative methods based on the
Lanczos process for the solution of linear systems
of equations as well as on the computation of bounds and estimates of the norm
of the error in the approximate solutions. These estimates are determined by
evaluating certain Gauss, anti-Gauss, or Gauss-Radau
quadrature rules.
These problems are very important in several applications, in particular to image processing and circuit design.
