Robust approximate inverse preconditioning for the conjugate gradient method

We present a variant of the AINV factorized sparse approximate inverse algo rithm which is applicable to any symmetric positive definite matrix. The ne w preconditioner is breakdown-free and, when used in conjunction with the c onjugate gradient method, results in a reliable solver for highly ill-condi tioned linear systems. We also investigate an alternative approach to a sta ble approximate inverse algorithm, based on the idea of diagonally compensa ted reduction of matrix entries. The results of numerical tests on challeng ing linear systems arising from finite element modeling of elasticity and d iffusion problems are presented.