Algorithms for Minimization Without DerivativesPrentice-Hall, 1972 - 195 sivua Outstanding text for graduate students and research workers proposes improvements to existing algorithms, extends their related mathematical theories, and offers details on new algorithms for approximating local and global minima. Many numerical examples, along with complete analysis of rate of convergence for most of the algorithms and error bounds that allow for the effect of rounding errors. |
Sisältö
PREFACE | xi |
THE USE OF SUCCESSIVE INTERPOLATION | 19 |
AN ALGORITHM WITH GUARANTEED | 47 |
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a₁ a₂ ALGOL 60 ALGOL procedures ALGOL W approximation BEGIN bisection Chapter Chebyquad Comp computed condition number d-unimodal defined definition Dekker's algorithm described in Section DIAGRAM effect of rounding eigenvalues equation example f is unimodal f(x₁ Fibonacci search Fletcher floating-point function evaluations required function f given in Section gives global minimum glomin2d golden section search Golub Hessian matrix INTEGER inverse quadratic interpolation iteration Lemma linear searches LONG REAL macheps matrix method minimization nonlinear number of function numerical results order at least order of convergence parabola parabolic interpolation points polynomial Powell Powell's problem procedure glomin procedure zero quadratic convergence quadratic function real procedure Rosenbrock rounding errors satisfies second derivative sequence singular value decomposition stopping criterion superlinear convergence Table Theorem 3.1 tion tolerance upper bound variables weak order x₁ Xn+1 Xn+g Xn+q zero2 δο λη