Abstract
LetH 1 andH 2 denote Hilbert spaces and suppose thatD is a subset ofH 1. This paper establishes the local and linear convergence of a general iterative technique for finding the zeros ofG:D→H 2 subject to the general constraintP(x)=x, whereP:D→D. The results are then applied to several classes of problems, including those of least squares, generalized eigenvalues, and constrained optimization. Numerical results are obtained as the procedure is applied to finding the zeros of polynomials in several variables.
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This work was supported by NSF grant G J 34737.
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McCormick, S.F. An iterative procedure for the solution of constrained nonlinear equations with application to optimization problems. Numer. Math. 23, 371–385 (1975). https://doi.org/10.1007/BF01437037
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DOI: https://doi.org/10.1007/BF01437037