Computational Methods for Numerical Analysis with R

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CRC Press, Taylor & Francis Group, 2017 - Numeraical Analysis - 257 pages
Cover -- Half title -- Aims and scope: -- Published Titles -- Title -- Copyright -- Dedication -- Contents -- List of Figures -- List of Tables -- List of R Functions -- Preface -- Chapter1 Introduction to Numerical Analysis -- 1.1 Numerical Analysis -- 1.1.1 The Goals of Numerical Analysis -- 1.1.2 Numerical Analysis in R -- 1.1.3 E ciency -- 1.2 Data Types in R -- 1.2.1 Data Types -- 1.2.2 Data Structures -- 1.3 Elementary Problems -- 1.3.1 Summation Algorithms -- 1.3.2 Evaluating Polynomials -- 1.3.3 The nth Root Algorithm -- Comments -- Exercises -- Chapter2 Error Analysis -- 2.1 True Values -- 2.1.1 Accuracy -- 2.1.2 Precision -- 2.2 Internal Data Storage -- 2.2.1 Binary Numbers -- 2.2.2 Floating Point Numbers -- 2.3 Numerical Error -- 2.3.1 Round-O Error and Machine -- 2.3.2 Loss of Signi cance -- 2.3.3 Over ow and Under ow -- 2.3.4 Error Propagation and Stability -- 2.4 Applications -- 2.4.1 Simple Division Algorithms -- 2.4.2 Binary Long Division -- Comments -- Exercises -- Chapter3 Linear Algebra -- 3.1 Vectors and Matrices -- 3.1.1 Vector and Matrix Operations -- 3.1.2 Elementary Row Operations -- 3.2 Gaussian Elimination -- 3.2.1 Row Echelon Form -- 3.2.2 Tridiagonal Matrices -- 3.3 Matrix Decomposition -- 3.3.1 LU Decomposition -- 3.3.2 Cholesky Decomposition -- 3.4 Iterative Methods -- 3.4.1 Jacobi Iteration -- 3.4.2 Gauss{Seidel Iteration -- 3.5 Applications -- 3.5.1 Least Squares -- Comments -- Exercises -- Chapter4 Interpolation and Extrapolation -- 4.1 Polynomial Interpolation -- 4.1.1 Linear Interpolation -- 4.1.2 Higher-Order Polynomial Interpolation -- 4.2 Piecewise Interpolation -- 4.2.1 Piecewise Linear Interpolation -- 4.2.2 Cubic Spline Interpolation -- 4.2.3 B ezier Curves -- 4.3 Multidimensional Interpolation -- 4.3.1 Bilinear Interpolation -- 4.3.2 Nearest Neighbor Interpolation -- 4.4 Applications

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