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Applied Numerical Analysis - Solutions manual by Curtis F. Gerald Patrick O. Wheatley

By Curtis F. Gerald Patrick O. Wheatley

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M. Wolfe, On the convergence of an algorithm for discrete Lp approximation, Numer. Math. 32 (1979) 439–459. S. Womersley, R. Fletcher, An algorithm for composite nonsmooth optimization problems, J. Optim. Theory Appl. 48 (1986) 493–523. W. Young, General theory of approximation by functions involving a given number of arbitrary parameters, Trans. Amer. Math. Soc. 8 (1907) 331–344. [209] Y. Zhang, A primal-dual interior point approach for computing the l1 and l∞ solutions of overdetermined linear systems, J.

B. Neilsen, A ÿnite smoothing algorithm for linear l1 estimation, SIAM J. Optim. 3 (1993) 223–235. [117] K. B. C. Pinar, New characterizations of l1 solutions of overdetermined linear systems, Operations Research Letters 16 (1994) 159–166. J. Maehly, Methods of ÿtting rational approximations, Part II, J. Assoc. Comput. Mach. 10 (1963) 257–266. C. Mairhuber, On Haar’s theorem concerning Chebyshev approximation problems having unique solutions, Proc. Amer. Math. Soc. 7 (1956) 609–615. T. Marti, A method for the numerical computation of best L1 approximations of continuous functions, Proceedings of Oberwolfach Conference, ISNM, Vol.

Fraser and Hart [70] in 1962, Werner [202] in 1962 and Stoer [186] in 1964 gave methods based on solving the system of nonlinear equations directly. In 1966, Curtis and Osborne [52] gave an algorithm which used the eigenvalue connection explicitly, solving the eigenvalue problem by inverse iteration with zero as an initial estimate for the eigenvalue; they also established quadratic convergence. Breuer [32] in 1987 suggested a di erent direct approach to this subproblem which used continued fraction interpolation, and which it was claimed can lead to a considerable increase in e ciency, and also accuracy and robustness.

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