Numerical Methods Using Java - For Data Science, Analysis, and Engineering

Implement numerical algorithms in Java using NM Dev, an object-oriented and high-performance programming library for mathematics. You'll see how it can help you easily create a solution for your complex engineering problem by quickly putting together classes. This book covers a wide range of to...

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Bibliographic Details
Main Author: Li, Haksun
Format: eBook Book
Language:English
Published: Berkeley, CA Apress, an imprint of Springer Nature 2022
Apress
Apress L. P
Edition:1
Subjects:
Big Data
Computer algorithms
Computer Science
COMPUTERS
General Engineering & Project Administration
General References
Information technology
Java (Computer program language)
Professional and Applied Computing
Professional Computing
Programming (Mathematics)
Programming Languages
Software Engineering
ISBN:1484267966, 9781484267967, 9781484267974, 1484267974
Online Access:Get full text
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Table of Contents:
  • Title Page Preface Table of Contents 1. Introduction to Numerical Methods in Java 2. Linear Algebra 3. Finding Roots of Equations 4. Finding Roots of System of Equations 5. Curve Fitting and Interpolation 6. Numerical Differentiation and Integration 7. Ordinary Differential Equations 8. Partial Differential Equations 9. Unconstrained Optimization 10. Constrained Optimization 11. Heuristics 12. Basic Statistics 13. Random Numbers and Simulation 14. Linear Regression 15. Time-Series Analysis References Index
  • 6.9.4. Gauss-Chebyshev Quadrature Formula -- 6.10. Integration by Substitution -- 6.10.1. Standard Interval -- 6.10.2. Inverting Variable -- 6.10.3. Exponential -- 6.10.4. Mixed Rule -- 6.10.5. Double Exponential -- 6.10.6. Double Exponential for Real Line -- 6.10.7. Double Exponential for Half Real Line -- 6.10.8. Power Law Singularity -- Chapter 7: Ordinary Differential Equations -- 7.1. Single-Step Method -- 7.1.1. Euler's Method (Polygon Method) -- 7.1.1.1. Euler's Formula -- 7.1.1.2. Implicit Euler Formula -- 7.1.1.3. Trapezoidal Formula -- 7.1.1.4. Prediction-Correction Method -- 7.1.2. Runge-Kutta Family -- 7.1.2.1. Second-Order Runge-Kutta Method -- 7.1.2.2. Third-Order Runge-Kutta Method -- 7.1.2.3. Higher-Order Runge-Kutta Method -- 7.1.3. Convergence -- 7.1.4. Stability -- 7.2. Linear Multistep Method -- 7.2.1. Adams-Bashforth Method -- 7.2.1.1. Adams-Bashforth Implicit Formulas -- 7.3. Comparison of Different Methods -- 7.4. System of ODEs and Higher-Order ODEs -- Chapter 8: Partial Differential Equations -- 8.1. Second-Order Linear PDE -- 8.1.1. Parabolic Equation -- 8.1.2. Hyperbolic Equation -- 8.1.3. Elliptic Equation -- 8.2. Finite Difference Method -- 8.2.1. Numerical Solution for Hyperbolic Equation -- 8.2.2. Numerical Solution for Elliptic Equation -- 8.2.2.1. Direct Transfer -- 8.2.2.2. Linear Interpolation -- 8.2.3. Numerical Solution for Parabolic Equation -- Chapter 9: Unconstrained Optimization -- 9.1. Brute-Force Search -- 9.2. C2OptimProblem -- 9.3. Bracketing Methods -- 9.3.1. Fibonacci Search Method -- 9.3.2. Golden-Section Search -- 9.3.3. Brent's Search -- 9.4. Steepest Descent Methods -- 9.4.1. Newton-Raphson Method -- 9.4.2. Gauss-Newton Method -- 9.5. Conjugate Direction Methods -- 9.5.1. Conjugate Directions -- 9.5.2. Conjugate Gradient Method -- 9.5.3. Fletcher-Reeves Method -- 9.5.4. Powell Method
  • 9.5.5. Zangwill Method -- 9.6. Quasi-Newton Methods -- 9.6.1. Rank-One Method -- 9.6.2. Davidon-Fletcher-Powell Method -- 9.6.3. Broyden-Fletcher-Goldfarb-Shanno Method -- 9.6.4. Huang Family (Rank One, DFP, BFGS, Pearson, McCormick) -- Chapter 10: Constrained Optimization -- 10.1. The Optimization Problem -- 10.1.1. General Optimization Algorithm -- 10.1.2. Constraints -- 10.1.2.1. Equality Constraints -- 10.1.2.2. Inequality Constraints -- 10.2. Linear Programming -- 10.2.1. Linear Programming Problems -- 10.2.2. First-Order Necessary Conditions -- 10.2.3. Simplex Method -- 10.2.4. The Algebra of Simplex Method -- 10.3. Quadratic Programming -- 10.3.1. Convex QP Problems with Only Equality Constraints -- 10.3.2. Active-Set Methods for Strictly Convex QP Problems -- 10.3.2.1. Primal Active-Set Method -- 10.3.2.2. Dual Active-Set Method -- 10.4. Semidefinite Programming -- 10.4.1. Primal and Dual SDP Problems -- 10.4.2. Central Path -- 10.4.3. Primal-Dual Path-Following Method -- 10.5. Second-Order Cone Programming -- 10.5.1. SOCP Problems -- 10.5.1.1. Portfolio Optimization -- 10.5.2. Primal-Dual Method for SOCP Problems -- 10.6. General Nonlinear Optimization Problems -- 10.6.1. SQP Problems with Only Equality Constraints -- 10.6.2. SQP Problems with Inequality Constraints -- Chapter 11: Heuristics -- 11.1. Penalty Function Method -- 11.2. Genetic Algorithm -- 11.2.1. Differential Evolution -- 11.3. Simulated Annealing -- Chapter 12: Basic Statistics -- 12.1. Random Variables -- 12.2. Sample Statistics -- 12.2.1. Mean -- 12.2.2. Weighted Mean -- 12.2.3. Variance -- 12.2.4. Weighted Variance -- 12.2.5. Skewness -- 12.2.6. Kurtosis -- 12.2.7. Moments -- 12.2.8. Rank -- 12.2.8.1. Quantile -- 12.2.8.2. Median -- 12.2.8.3. Maximum and Minimum -- 12.2.9. Covariance -- 12.2.9.1. Sample Covariance -- 12.2.9.2. Correlation
  • 12.2.9.3. Covariance Matrix and Correlation Matrix -- 12.2.9.4. Ledoit-Wolf Linear Shrinkage -- 12.2.9.5. Ledoit-Wolf Nonlinear Shrinkage -- 12.3. Probability Distribution -- 12.3.1. Moments -- 12.3.2. Normal Distribution -- 12.3.3. Log-Normal Distribution -- 12.3.4. Exponential Distribution -- 12.3.5. Poisson Distribution -- 12.3.6. Binomial Distribution -- 12.3.7. T-Distribution -- 12.3.8. Chi-Square Distribution -- 12.3.9. F-Distribution -- 12.3.10. Rayleigh Distribution -- 12.3.11. Gamma Distribution -- 12.3.12. Beta Distribution -- 12.3.13. Weibull Distribution -- 12.3.14. Empirical Distribution -- 12.4. Multivariate Probability Distributions -- 12.4.1. Multivariate Normal Distribution -- 12.4.2. Multivariate T-Distribution -- 12.4.3. Multivariate Beta Distribution -- 12.4.4. Multinomial Distribution -- 12.5. Hypothesis Testing -- 12.5.1. Distribution Tests -- 12.5.1.1. Normality Test -- Shapiro-Wilk Test -- Jarque-Bera Test -- D'Agostino Test -- Lilliefors Test -- 12.5.1.2. Kolmogorov Test -- 12.5.1.3. Anderson-Darling Test -- 12.5.1.4. Cramer Von Mises Test -- 12.5.1.5. Pearson's Chi-Square Test -- 12.5.2. Rank Test -- 12.5.2.1. T-Test -- 12.5.2.2. One-Way ANOVA Test -- 12.5.2.3. Kruskal-Wallis Test -- 12.5.2.4. Wilcoxon Signed Rank Test -- 12.5.2.5. Siegel-Tukey Test -- 12.5.2.6. Van der Waerden Test -- 12.6. Markov Models -- 12.6.1. Discrete-Time Markov Chain -- 12.6.2. Hidden Markov Model -- 12.6.2.1. The Likelihood Question -- 12.6.2.2. The Decoding Question -- 12.6.2.3. The Learning Question -- 12.7. Principal Component Analysis -- 12.8. Factor Analysis -- 12.9. Covariance Selection -- Chapter 13: Random Numbers and Simulation -- 13.1. Uniform Random Number Generators -- 13.1.1. Linear Congruential Methods -- 13.1.2. Mersenne Twister -- 13.2. Sampling from Probability Distribution -- 13.2.1. Inverse Transform Sampling
  • 13.2.2. Acceptance-Rejection Sampling
  • 3.4.1. Linear Interpolation Method, False Position Method, Secant Method -- 3.4.2. Inverse Quadratic Interpolation -- 3.4.3. Brent's Method Implementation -- 3.5. The Newton-Raphson Method -- 3.5.1. Halley's Method -- Chapter 4: Finding Roots of System of Equations -- 4.1. System of Equations -- 4.2. Finding Roots of Systems of Two Nonlinear Equations -- 4.3. Finding Roots of Systems of Three or More Equations -- Chapter 5: Curve Fitting and Interpolation -- 5.1. Least Squares Curve Fitting -- 5.2. Interpolation -- 5.2.1. Linear Interpolation -- 5.2.2. Cubic Hermite Spline Interpolation -- 5.2.3. Cubic Spline Interpolation -- 5.2.4. Newton Polynomial Interpolation -- Linear Form -- Quadratic Form -- General Form -- 5.3. Multivariate Interpolation -- 5.3.1. Bivariate Interpolation -- 5.3.2. Multivariate Interpolation -- Chapter 6: Numerical Differentiation and Integration -- 6.1. Numerical Differentiation -- 6.2. Finite Difference -- 6.2.1. Forward Difference -- 6.2.2. Backward Difference -- 6.2.3. Central Difference -- 6.2.4. Higher-Order Derivatives -- 6.3. Multivariate Finite Difference -- 6.3.1. Gradient -- 6.3.2. Jacobian -- 6.3.3. Hessian -- 6.4. Ridders' Method -- 6.5. Derivative Functions of Special Functions -- 6.5.1. Gaussian Derivative Function -- 6.5.2. Error Derivative Function -- 6.5.3. Beta Derivative Function -- 6.5.4. Regularized Incomplete Beta Derivative Function -- 6.5.5. Gamma Derivative Function -- 6.5.6. Polynomial Derivative Function -- 6.6. Numerical Integration -- 6.7. The Newton-Cotes Family -- 6.7.1. The Trapezoidal Quadrature Formula -- 6.7.2. The Simpson Quadrature Formula -- 6.7.3. The Newton-Cotes Quadrature Formulas -- 6.8. Romberg Integration -- 6.9. Gauss Quadrature -- 6.9.1. Gauss-Legendre Quadrature Formula -- 6.9.2. Gauss-Laguerre Quadrature Formula -- 6.9.3. Gauss-Hermite Quadrature Formula
  • Intro -- Table of Contents -- About the Author -- About the Technical Reviewer -- Acknowledgments -- Preface -- Chapter 1: Introduction to Numerical Methods in Java -- 1.1. Library Design -- 1.1.1. Class Parsimony -- 1.1.2. Java vs. C++ Performance -- 1.2. Setup -- 1.2.1. Installing the Java Development Kit -- 1.2.2. NetBeans with Maven -- 1.2.3. nmdev.jar -- 1.2.4. IntelliJ IDEA -- 1.2.5. SuanShu -- 1.3. About This Book -- 1.3.1. Sample Code -- Chapter 2: Linear Algebra -- 2.1. Vector -- 2.1.1. Element-Wise Operations -- 2.1.2. Norm -- 2.1.3. Inner Product and Angle -- 2.2. Matrix -- 2.2.1. Matrix Operations -- 2.2.2. Element-Wise Operations -- 2.2.3. Transpose -- 2.2.4. Matrix Multiplication -- 2.2.5. Rank -- 2.2.6. Determinant -- 2.2.7. Inverse and Pseudo-Inverse -- 2.2.8. Kronecker Product -- 2.3. Matrix Decomposition -- 2.3.1. LU Decomposition -- 2.3.2. Cholesky Decomposition -- 2.3.3. Hessenberg Decomposition and Tridiagonalization -- 2.3.4. QR Decomposition -- 2.3.5. Eigen Decomposition -- 2.3.6. Singular Value Decomposition -- 2.4. System of Linear Equations -- 2.4.1. Row Echelon Form and Reduced Row Echelon Form -- 2.4.2. Back Substitution -- 2.4.3. Forward Substitution -- 2.4.4. Elementary Operations -- 2.4.4.1. Row Switching Transformation -- 2.4.4.2. Row Multiplying Transformation -- 2.4.4.3. Row Addition Transformation -- 2.4.5. Gauss Elimination and Gauss-Jordan Elimination -- 2.4.6. Homogeneous and Nonhomogeneous Systems -- 2.4.7. Over-Determined Linear System -- 2.5. Sparse Matrix -- 2.5.1. Dictionary of Keys -- 2.5.2. List of Lists -- 2.5.3. Compressed Sparse Row -- 2.5.4. Sparse Matrix/Vector Operations -- 2.5.5. Solving Sparse Matrix Equations -- Chapter 3: Finding Roots of Equations -- 3.1. An Equation of One Variable -- 3.2. Jenkins-Traub Algorithm -- 3.3. The Bisection Method -- 3.4. Brent's Method