Titlebook: Krylov Methods for Nonsymmetric Linear Systems; From Theory to Compu Gérard Meurant,Jurjen Duintjer Tebbens Book 2020 Springer Nature Switz

TSH582

不能平靜

記憶法

Numerical comparisons of methods,In this chapter we compare numerically some of the methods we have studied in the previous chapters. We chose the methods which seem the most interesting ones and the most widely used.

嘮叨

BADGE

Methods equivalent to FOM or GMRES,l norms. However, as we will see, this is not always the case in finite precision arithmetic. The algorithms mathematically equivalent to GMRES either construct residual vectors . orthogonal to . or explicitly minimize the residual norms.

反復(fù)拉緊

Transpose-free Lanczos methods,ix-vector product with . (or .). In this chapter we study iterative methods, derived from those of Chapter 8, that do not need a multiplication with the transpose of .. They are sometimes called product-type or transpose-free methods. We consider, particularly, CGS and BiCGStab and their variants.

用肘

Restart, deflation and truncation,rrences to compute the basis vectors. These techniques are restarting and truncation. For restarting, we describe methods like GMRES-DR which is using approximate eigenvectors for computing the restarting vectors.

碎石

Q-OR and Q-MR methods,imension grows with the iteration number. Most popular Krylov methods can be classified as either a quasi-orthogonal residual (Q-OR) method or a quasi-minimal residual (Q-MR) method, with most Q-OR methods having Q-MR analogs; see [296].

妨礙

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