Preconditioning Techniques for Sparse Linear Systems

Preconditioning Techniques for Sparse Linear Systems

Combinatorial Preconditioning for Sparse Linear Systems

A key ingredient in the solution of a large, sparse system of linear equations by an iterative method like conjugate gradients is a preconditioner, which is in a sense an approximation to the matrix of coefficients. Ideally, the iterative method converges much faster on the preconditioned system at the extra cost of one solve against the preconditioner per iteration. We survey a little-known te...

Some Preconditioning Techniques for Linear Systems

New convergence intervals of parameters αi are derived and applied for solving the modified linear systems, which enables a better understanding of how parameters should be chosen. The convergence theorem for H-matrix is given. Meanwhile, we discuss the convergence results forM -matrices linear systems and give some new preconditioners. Numerical examples are used to illustrate our results. Key...

Parallel Multilevel Block ILU Preconditioning Techniques for Large Sparse Linear Systems

We present a class of parallel preconditioning strategies built on a multilevel block incomplete LU (ILU) factorization technique to solve large sparse linear systems on distributed memory parallel computers. The preconditioners are constructed by using the concept of block independent sets. Two algorithms for constructing block independent sets of a distributed sparse matrix are proposed. We c...

Parallel two level block ILU preconditioning techniques for solving large sparse linear systems

We discuss issues related to domain decomposition and multilevel preconditioning techniques which are often employed for solving large sparse linear systems in parallel computations. We introduce a class of parallel preconditioning techniques for general sparse linear systems based on a two level block ILU factorization strategy. We give some new data structures and strategies to construct loca...