Abstract: As we saw in the previous chapter, there exist two types of methods to solve systems of equations with short recurrence relations: (1) minimization algorithms, such as the conjugate gradient type algorithms, and (2) Lanczos-type algorithms. The short recurrence and the minimization properties have been shown to hold for the conjugate gradient methods for matrices that are selfadjoint and positive definite w.r.t. to the inner product used in the algorithm. The short recurrence holds for the biconjugate gradient-type Lanczos algorithms, also for nonsymmetric matrices, but these algorithms can break down when the matrix is indefinite.
Publication Year: 1994
Publication Date: 1994-03-25
Language: en
Type: book-chapter
Indexed In: ['crossref']
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Cited By Count: 11
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