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A. van der Vorst / Journal of Computational and Applied Mathematics 123 (2000) 35–65 5. 4]. The Jacobi method which was originally proposed in 1846 [65], reduces a real symmetric matrix to diagonal form by a sequence of plane rotations. Jacobi, however, did not use the method to full convergence, as was done in the 20th century, but combined it with an iterative process (Gauss–Jacobi iterations) for the missing component of the desired eigenvector (for which he took a unit vector as an initial guess).

Kamath, A. Sameh, A projection method for solving nonsymmetric linear systems on multiprocessors, Parallel Comput. 9 (1988=89) 291–312. [109] S. Kaniel, Estimates for some computational techniques in linear algebra, Math. Comp. 20 (1966) 369–378. [110] L. Kantorovitch, On an e cient method for solving optimization problems for quadratic functionals, DAN SSSR 48(7) (1945) 7–8 (in Russian). [111] W. Karush, Convergence of a method of solving linear problems, Proc. Amer. Math. Soc. 3 (1952) 839–851.

Users of iterative techniques are really split in two camps: those who use exclusively multigrid methods and those who use exclusively (preconditioned) Krylov subspace methods. 3, but this is an exception rather than a rule. When multigrid techniques work, they can be extremely e cient – far more so than preconditioned Krylov methods. However, their e ciency relies essentially on the inter-level restriction, and prolongation operators, the choice of which will vary from one application to the next.

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