Topics in Validated Computations: Proceedings of IMACS-GAMM International Workshop on Validated Computation, Oldenburg, Germany, 30 August-3 September 1993Jürgen Herzberger This text provides the interval analysis community with surveys of important recent developments in the creation of validated numerical algorithms. In addition, the publication informs the numerical analysts and appliers of numerical software about the enormous variety of problem-solving algorithms now available, even for sophisticated problems which were beyond reach at the beginning of research some two decades ago. Contributions are sourced from a variety of international experts and together these form a textbook collection of 14 non-overlapping multidisciplinary sections. in interval arithmetic, whilst the concluding chapter offers instructions on how to implement interval algorithms. Other problem areas addressed in the bulk of the volume include: systems of nonlinear equations, simultaneous methods for polynomial zeros, linear systems, matrix inversion, matrix eigenvalue problems, eigenvalues of selfadjoint problems, ODE's, PDE's, optimization, problems in engineering, and complexity considerations in linear interval problems. |
Contents
Basic definitions and properties of interval arithmetic J Herzberger | 1 |
Validated computation of polynomial zeros by the DurandKerner 27 | 27 |
method T Yamamoto S Kanno and L Atanassova | 55 |
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Common terms and phrases
A₁ Alefeld algebraic algorithm Angew applied approximate solution assertion assume assumption boundary value problems branch and bound calculated components Computer Arithmetic condition contains convergence defined denote differential equations Durand-Kerner method eigenvalue problem eigenvectors error bounds evaluation example exists given global minimum point HB(N Hence Herzberger holds hyperpower hyperpower method implies inclusion function inclusion methods inequality input data interval arithmetic interval matrix interval operations interval vector inverse inverse-positive iterative methods Kulisch Lemma linear programming linear programming problems linear systems lower bound Math matrix norm Mech monotonicity multiplications nonlinear nonsingular norm NP-hard numerical obtain parameters Pascal-XSC polynomial positive definite Proof proved regular rounding errors satisfied Scientific Computation Section sequence singular value step symmetric t₁ Theorem Theorem 2.1 unique Universität upper bound verified width yields zero