We consider symmetric preconditioning strategies for the iterative solution of dense complex symmetric non-Hermitian systems arising in computational electromagnetics. In particular we report on the numerical behaviour of the classical Incomplete Cholesky factorization as well as some of its recent variants and consider also well known factorized approximate inverses. We illustrate the difficul...

Incomplete Cholesky factorizations have long been important as preconditioners for use in solving largescale symmetric positive-definite linear systems. In this paper, we focus on the relationship between two important positive semidefinite modification schemes that were introduced to avoid factorization breakdown, namely the approach of Jennings and Malik and that of Tismenetsky. We present a ...

Incomplete Cholesky factorisation based preconditioners have been widely used in association with the Conjugate Gradient Method. The standard incomplete Cholesky factorisation, or IC(0) factorisation, forces the Cholesky factor L (where A LL T) to have the same sparsity as A. Two main strategies exist for controlling the amount of ll; namely control based upon position (or ll level) and control...

We propose variants of the modified incomplete Cholesky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

The present paper is dedicated to the preconditioning of boundary element matrices in wavelet coordinates. We investigate the incomplete Cholesky factorization for a pattern which includes also the coefficients of all off-diagonal bands associated with the level-level-interactions. The pattern is chosen in such a way that the incomplete Cholesky factorization is computable in log-linear complex...