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Introduction to Interval Computation
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In this paper, the authors present an ALGOLGOL-based approach for the inclusion of complex Zeros of polynomials of a function of one real variable in a system of linear systems of equations.Abstract:
Preface to the English Edition. Preface to the German Edition. Real Interval Arithmetic. Further Concepts and Properties. Interval Evaluation and Range of Real Functions. Machine Interval Arithmetic. Complex Interval Arithmetic. Metric, Absolute, Value, and Width in. Inclusion of Zeros of a Function of One Real Variable. Methods for the Simultaneous Inclusion of Real Zeros of Polynomials. Methods for the Simultaneous Inclusion of Complex Zeros of Polynomials. Interval Matrix Operations. Fixed Point Iteration for Nonlinear Systems of Equations. Systems of Linear Equations Amenable to Interation. Optimality of the Symmetric Single Step Method with Taking Intersection after Every Component. On the Feasibility of the Gaussian Algorithm for Systems of Equations with Intervals as Coefficients. Hansen's Method. The Procedure of Kupermann and Hansen. Ireation Methods for the Inclusion of the Inverse Matrix and for Triangular Decompositions. Newton-like Methods for Nonlinear Systems of Equations. Newton-like Methods without Matrix Inversions. Newton-like Methods for Particular Systems of Nonlinear Equations. Newton-like Total step and Single Step Methods. Appendix A. The Order of Convergence of Iteration Methods in vn(Ic) and Mmn(iC) ). Appendix B. Realizations of Machine Interval Arithmetics in ALGOL 60. Appendix C. ALGOL Procedures. Bibliography. Index of Notation. Subject Index.read more
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References
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Book
Introduction to Interval Analysis
TL;DR: This unique book provides an introduction to a subject whose use has steadily increased over the past 40 years, and provides broad coverage of the subject as well as the historical perspective of one of the originators of modern interval analysis.
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Interval methods for systems of equations
TL;DR: In this paper, the authors describe the basic properties of interval arithmetic and the solution of square linear systems of equations, and the Hull computation of nonlinear systems of equation 6, 7, 8.
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Global optimization using interval analysis
TL;DR: This Second Edition of Global Optimization Using Interval Analysis expands and improves various aspects of its forerunner and features significant new discussions, such as those on the use of consistency methods to enhance algorithm performance.
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The polynomial-time hierarchy☆
TL;DR: The problem of deciding validity in the theory of equality is shown to be complete in polynomial-space, and close upper and lower bounds on the space complexity of this problem are established.