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k-Step iterative methods for solving nonlinear systems of equations (1986)

Gutknecht, M. H. ; Niethammer, W. ; Varga, R. S.

Springer

Numerische Mathematik 48 (1986), S. 699-712

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Details

ISSN: 0945-3245

Keywords: AMS(MOS): 65H10 ; 65F10 ; CR: G15 ; G1.3

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Summary LetΦ: ℂ n →ℂ n be Fréchet differentiable, and let the equation (1) $$x = \Phi \left( x \right)$$ have at least one fixed point. We considerk-step stationary iterative methods (2) $$y_m : = \mu _0 \Phi \left( {y_{m - 1} } \right) + \mu _1 y_{m - 1} + ... + \mu _k y_{m - k} , m \geqq k,$$ withμ 0+μ 1+...+μ k =1. Using results for an affine mappingΦ: ℂ n →ℂ n , it is proven that (2) may converge locally even in cases where the usual iterationx m =Φ(x m−1) belonging to (1) diverges. These results are extended to nonstationary methods of type (2) and to “cyclic” mappings.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01399689

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