Many statistical applications require the solution of a symmetric positive de57356nite covariance matrix sometimes with a large number of righthand sides of a statistical independence nature With preconditioning the preconditioned matrix has almost ID: 74755
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0 200 400 600 800 1000 10-4 10-2 100 102 0 200 400 600 800 1000 10-4 10-2 100 102 104 0 200 400 600 800 1000 10-6 10-4 10-2 100 102 0 200 400 600 800 1000 10-5 100 105 0 20 40 60 80 100 10-10 10-8 10-6 10-4 10-2 100 102 104 PCG block PCG deflated PCG deflated block PCG 0 20 40 60 80 100 10-10 10-8 10-6 10-4 10-2 100 102 PCG block PCG deflated PCG deflated block PCG 0 20 40 60 80 100 10-8 10-6 10-4 10-2 100 102 CG block CG deflated CG deflated block CG 0 20 40 60 80 100 10-8 10-6 10-4 10-2 100 102 CG block CG deflated CG deflated block CG 103 104 102 103 104 105 106 matrix size ntime (seconds) 103 104 102 103 104 105 matrix size ntime (seconds)