ISSN:
1573-2878
Keywords:
Operator equations
;
Banach spaces
;
iterative methods
;
existence
;
rate of convergence
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract LetM 0, characterized byx k+1=G 0(x k),k⩾0,x 0 prescribed, be an iterative method for the solution of the operator equationF(x)=0, whereF:X → X is a given operator andX is a Banach space. Let ω:X → X be a given operator, and let the methodM mbe characterized byx x+1,m =G m(x k,m),k⩾0,x 0,m prescribed, where $$G_i (x) = G_0 (x) - \sum\limits_{j = 0}^{i - 1} { F'(\omega (x))^{ - 1} F(G_j (x)), i = 1, . . . ,m,} $$ in whichG 0:X → X is a given operator andF′:X → L(X) is the Fréchet derivative ofF. Sufficient conditions for the existence of a solutionx* m ofF(x)=0 to which the sequence (x k,m) generated from methodM mconverges are given, together with a rate-of-convergence estimate.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934795
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