TY - JOUR

T1 - Krylov subspace methods for solving large unsymmetric linear systems

AU - Saad, Y.

PY - 1981/7

Y1 - 1981/7

N2 - Some algorithms based upon a projection process onto the Krylov subspace are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldis algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace Km and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.

AB - Some algorithms based upon a projection process onto the Krylov subspace are developed, generalizing the method of conjugate gradients to unsymmetric systems. These methods are extensions of Arnoldis algorithm for solving eigenvalue problems. The convergence is analyzed in terms of the distance of the solution to the subspace Km and some error bounds are established showing, in particular, a similarity with the conjugate gradient method (for symmetric matrices) when the eigenvalues are real. Several numerical experiments are described and discussed.

UR - http://www.scopus.com/inward/record.url?scp=84966222159&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84966222159&partnerID=8YFLogxK

U2 - 10.1090/S0025-5718-1981-0616364-6

DO - 10.1090/S0025-5718-1981-0616364-6

M3 - Article

AN - SCOPUS:84966222159

SN - 0025-5718

VL - 37

SP - 105

EP - 126

JO - Mathematics of Computation

JF - Mathematics of Computation

IS - 155

ER -