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