UID:
almahu_9949865637002882
Format:
1 online resource (257 pages) :
,
illustrations
Edition:
1.
ISBN:
1498723640
,
9781498723640
,
9781315120195
,
1315120194
,
9781498723633
,
1498723632
Series Statement:
Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series
Content:
Computational Methods for Numerical Analysis with R is an overview of traditional numerical analysis topics presented using R. This guide shows how common functions from linear algebra, interpolation, numerical integration, optimization, and differential equations can be implemented in pure R code. Every algorithm described is given with a complete function implementation in R, along with examples to demonstrate the function and its use. Computational Methods for Numerical Analysis with R is intended for those who already know R, but are interested in learning more about how the underlying algorithms work. As such, it is suitable for statisticians, economists, and engineers, and others with a computational and numerical background. --
Note:
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.
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2.2 Internal Data Storage2.2.1 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.
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3.3.2 Cholesky Decomposition3.4 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; 4.4.1 Time Series Interpolation.
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4.4.2 Computer GraphicsComments; Exercises ; Chapter5 Differentiation and Integration; 5.1 Numerical Di erentiation; 5.1.1 Finite Di erences; 5.1.2 The Second Derivative; 5.2 Newton{Cotes Integration; 5.2.1 Multipanel Interpolation Rules; 5.2.2 Newton{Cotes Errors; 5.2.3 Newton{Cotes Forms, Generally; 5.3 Gaussian Integration; 5.3.1 The Gaussian Method; 5.3.2 Implementation Details; 5.4 More Techniques; 5.4.1 Adaptive Integrators; 5.4.2 Romberg's Method; 5.4.3 Monte Carlo Methods; 5.5 Applications; 5.5.1 Revolved Volumes; 5.5.2 Gini Coe cients; Comments; Exercises.
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Chapter6 Root Finding and Optimization6.1 One-Dimensional Root Finding; 6.1.1 Bisection Method; 6.1.2 Newton{Raphson Method; 6.1.3 Secant Method; 6.2 Minimization and Maximization; 6.2.1 Golden Section Search; 6.2.2 Gradient Descent; 6.3 Multidimensional Optimization; 6.3.1 Multidimensional Gradient Descent; 6.3.2 Hill Climbing; 6.3.3 Simulated Annealing; 6.4 Applications; 6.4.1 Least Squares; 6.4.2 The Traveling Salesperson; Comments; Exercises; Chapter7 Differential Equations; 7.1 Initial Value Problems; 7.1.1 Euler Method ; 7.1.2 Runge{Kutta Methods, Generally.
Additional Edition:
Print version: ISBN 9781498723633
Language:
English
URL:
https://www.taylorfrancis.com/books/9781315120195
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