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We present a new convergence analysis of popular Broyden’s method in the Banach/Hilbert space setting which is applicable to non- smooth operators. Moreover, we do not assume a priori solvability of the equation under consideration. Nevertheless, without these simplifying as- sumptions our convergence theorem implies existence of a solution and superlinear convergence of Broyden’s iterations. To demonstrate practi- cal merits of Broyden’s method, we use it for numerical solution of three nontrivial infinite-dimensional problems.
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참고문헌 (22)
참고문헌 신청
A. Galperin / 2006 / Secant method with regularly continuous divided differences / J. Comput. Appl. Math 193 (2) : 574 ~ 595
A. Galperin / 2007 / On a class of systems of difference equations and their invariants / J. Difference Equ. Appl 13 (5) : 357 ~ 381
A. Galperin / 2009 / Ulm’s method without derivatives / Nonlinear Anal 71 (5-6) : 2094 ~ 2113
A. Griewank / 1987 / The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert space / SIAM J. Numer. Anal 24 (3) : 684 ~ 705
C. G. Broyden / 1965 / A class of methods for solving nonlinear simultaneous equations / Math. Comp 19 : 577 ~ 593
A. Galperin / 2007 / On a class of systems of difference equations and their invariants / J. Difference Equ. Appl 13 (5) : 357 ~ 381
A. Galperin / 2009 / Ulm’s method without derivatives / Nonlinear Anal 71 (5-6) : 2094 ~ 2113
A. Griewank / 1987 / The local convergence of Broyden-like methods on Lipschitzian problems in Hilbert space / SIAM J. Numer. Anal 24 (3) : 684 ~ 705
C. G. Broyden / 1965 / A class of methods for solving nonlinear simultaneous equations / Math. Comp 19 : 577 ~ 593
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