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Mathematics of Computation

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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, Wiley, New York, 1973. MR 0423815 (54:11789)
  • [4] W. Murray, Numerical Methods for Unconstrained Optimization, Academic Press, New York, 1972.
  • [5] V. Pereyra, ``Accelerating the convergence of discretization algorithms,'' SIAM J. Numer. Anal., v. 4, 1967, pp. 508-533. MR 0221726 (36:4778)
  • [6] D. M. Ryan, ``Penalty and barrier functions,'' in Numerical Methods for Constrained Optimization (P. E. Gill and W. Murray, Eds.), Academic Press, New York, 1974. MR 0456505 (56:14729)
  • [7] A. H. Sherman, ``On Newton-iterative methods for the solution of systems of nonlinear equations,'' SIAM J. Numer. Anal., v. 15, 1978, pp. 755-771. MR 0483382 (58:3388)

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Keywords: Iteration, fixed point iteration, efficiency, numerical analysis
Article copyright: © Copyright 1982 American Mathematical Society

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