Titlebook: Numerical Toolbox for Verified Computing I; Basic Numerical Prob Ulrich Kulisch,Rolf Hammer,Matthias Hocks Book 1993 Springer-Verlag Berlin

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Evaluation of Polynomials as to be practically useless. Roundoff and cancellation errors are especially dangerous if we are evaluating a function close to a root, as we will see in Chapter 9 when we compute verified enclosures of zeros of polynomials.

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Global Optimizationle, so valleys, no matter how narrow, are recognized with certainty. Further, interval techniques often can reject large regions in which the optimum can be guaranteed not to lie, so they can be faster overall than classical methods for many problems.

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Automatic Differentiation for Gradients, Jacobians, and Hessiansomputation of numerical values, combining the advantages of symbolic and numerical differentiation. Only the algorithm or formula for the function is required. No explicit formulas for the gradient, Jacobian, or Hessian have to be derived and coded.

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Nonlinear Systems of Equations and it delivers information about existence and uniqueness of the computed solutions. The method we present is a variant of the . based on the method of Hansen and Sengupta [3], [29], and a modification of Ratz [73]. Our method makes use of the extended interval operations defined in Section 3.3.

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玩忽职守

Book 1993erical problems with a verification of the results. We use the features of the scientific computer language PASCAL-XSC to offer modules that can be combined by the reader to his/her individual needs. Our overriding concern is reliability - the automatic verification of the result a computer returns

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