Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

Fixed point iteration with inexact function values


Author: Peter Alfeld
Journal: Math. Comp. 38 (1982), 87-98
MSC: Primary 65H10; Secondary 65K10
MathSciNet review: 637288
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Abstract: In many iterative schemes, the precision of each step depends on the computational effort spent on that step. A method of specifying a suitable amount of computation at each step is described. The approach is adaptive and aimed at minimizing the overall computational cost subject to attaining a final iterate that satisfies a suitable error criterion. General and particular cost functions are considered, and a numerical example is given.


References [Enhancements On Off] (What's this?)

  • [1] R. S. Dembo, S. C. Eisenstat & T. Steihaug, Inexact Newton Methods, Working Paper #47 (Series B), Yale School of Organization and Management, 1980.
  • [2] A. C. Hearn, REDUCE User's Manual, 2nd ed., Report UCP-19, Department of Computer Science, University of Utah, 1973.
  • [3] J. D. Lambert, Computational methods in ordinary differential equations, John Wiley & Sons, London-New York-Sydney, 1973. Introductory Mathematics for Scientists and Engineers. MR 0423815
  • [4] W. Murray, Numerical Methods for Unconstrained Optimization, Academic Press, New York, 1972.
  • [5] Victor Pereyra, Accelerating the convergence of discretization algorithms, SIAM J. Numer. Anal. 4 (1967), 508–533. MR 0221726
  • [6] D. M. Ryan, Penalty and barrier functions, Numerical methods for constrained optimization (Proc. Sympos., National Physical Lab., Teddington, 1974) Academic Press, London, 1974, pp. 175–190. MR 0456505
  • [7] Andrew H. Sherman, On Newton-iterative methods for the solution of systems of nonlinear equations, SIAM J. Numer. Anal. 15 (1978), no. 4, 755–771. MR 0483382

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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1982-0637288-5
Keywords: Iteration, fixed point iteration, efficiency, numerical analysis
Article copyright: © Copyright 1982 American Mathematical Society