Barrett R.Templates for the solution of linear systems.Building blocks for iterative methods

124

matrix-vector products, 78{79 vector updates, 78

preconditioners, 39{55 ADI, 54{55

parallelism in, 55

block factorizations, 49{52 block tridiagonal, 51 central di erences, 46 cost, 39{40

fast solvers, 54

incomplete factorization, 43{52 left, 40

point incomplete factorizations, 44{49

ll-in strategies, 45 modi ed, 46{47 parallelism in, 48{49 vectorization of, 47 wavefronts in, 47{49

point Jacobi, 41{42 polynomial, 52{53 reduced system, 85{86 right, 40

SSOR, 42 parallelism in, 42

symmetric part, 53{54

QMR method, see method, QMR Quasi-Minimal Residual method, see

method, QMR

relaxation method, see method, relaxation

residuals

in BiCG, 21

in CG, 14 orthogonality of, 14

in SYMMLQ orthogonality of, 17

restarting

in BiCG, 23

in GMRES, 19, 21

row projection methods, 92{93

search directions in BiCG, 21 in CG, 14, 15

A-orthogonality of, 14

INDEX

smooth convergence, see convergence, smooth

software

obtaining, 95{96

SOR method, see method, SOR sparse matrix storage, 64{68

BCRS, 65

CCS, 65 CDS, 65{67 CRS, 64{65 JDS, 67{68 SKS, 68

SSOR method, see method, SSOR stalled convergence, see convergence,

stalled Stationary methods, 7{14 stopping criteria, 57{63

Successive Overrelaxation method, see method, SOR

superlinear convergence, see convergence, superlinear

Symmetric LQ method, see method, SYMMLQ

Symmetric Successive Overrelaxation method, see method, SSOR

SYMMLQ method, see method, SYMMLQ

template, 1 three-term recurrence

in CG, 15 two-term recurrence, 25

underrelaxation, 11

wavefronts, see preconditioners, point incomplete factorizations, wavefront