دانلود کتاب Interval Analysis: and Automatic Result Verification

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Preface\n Contents\n1 Preliminaries\n 1.1 Notations and basic definitions\n 1.2 Metric spaces\n 1.3 Normed linear spaces\n 1.4 Polynomials\n 1.5 Zeros and fixed points of functions\n 1.6 Mean value theorems\n 1.7 Normal forms of matrices\n 1.8 Eigenvalues\n 1.9 Nonnegative matrices\n 1.10 Particular matrices\n2 Real intervals\n 2.1 Intervals, partial ordering\n 2.2 Interval arithmetic\n 2.3 Algebraic properties, χ -function\n 2.4 Auxiliary functions\n 2.5 Distance and topology\n 2.6 Elementary interval functions\n 2.7 Machine interval arithmetic\n3 Interval vectors, interval matrices\n 3.1 Basics\n 3.2 Powers of interval matrices\n 3.3 Particular interval matrices\n4 Expressions, P-contraction, ε-inflation\n 4.1 Expressions, range\n 4.2 P-contraction\n 4.3 ε-inflation\n5 Linear systems of equations\n 5.1 Motivation\n 5.2 Solution sets\n 5.3 Interval hull\n 5.4 Direct methods\n 5.5 Iterative methods\n6 Nonlinear systems of equations\n 6.1 Newton method – one-dimensional case\n 6.2 Newton method – multidimensional case\n 6.3 Krawczyk method\n 6.4 Hansen–Sengupta method\n 6.5 Further existence tests\n 6.6 Bisection method\n7 Eigenvalue problems\n 7.1 Quadratic systems\n 7.2 A Krawczyk-like method\n 7.3 Lohner method\n 7.4 Double or nearly double eigenvalues\n 7.5 The generalized eigenvalue problem\n 7.6 A method due to Behnke\n 7.7 Verification of singular values\n 7.8 An inverse eigenvalue problem\n8 Automatic differentiation\n 8.1 Forward mode\n 8.2 Backward mode\n9 Complex intervals\n 9.1 Rectangular complex intervals\n 9.2 Circular complex intervals\n 9.3 Applications of complex intervals\nFinal Remarks\nAppendix\n A Jordan normal form\n B Brouwer’s fixed point theorem\n C Theorem of Newton–Kantorovich\n D The row cyclic Jacobi method\n E The CORDIC Algorithm\n F The symmetric solution set\n G INTLAB\nBibliography\nSymbol Index\nAuthor Index\nSubject Index