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· 제목 : Numerical Methods Using Java: For Data Science, Analysis, and Engineering (Paperback)
· 분류 : 외국도서 > 컴퓨터 > 데이터베이스 관리 > 일반
· ISBN : 9781484267967
· 쪽수 : 1186쪽
· 출판일 : 2022-01-06
· 분류 : 외국도서 > 컴퓨터 > 데이터베이스 관리 > 일반
· ISBN : 9781484267967
· 쪽수 : 1186쪽
· 출판일 : 2022-01-06
목차
Table of Contents
About the Authors...........................................................................................................i
Preface............................................................................................................................ii
1. Why Java?..............................................................................................................6
1.1. Java in 2020.....................................................................................................6
1.2. Java vs. C++....................................................................................................6
1.3. Java vs. Python................................................................................................6
1.4. Java in the future .............................................................................................6
2. Data Structures.......................................................................................................7
2.1. Function...........................................................................................................72.2. Polynomial ......................................................................................................7
3. Linear Algebra .......................................................................................................8
3.1. Vector and Matrix ...........................................................................................8
3.1.1. Vector Properties .....................................................................................8
3.1.2. Element-wise Operations.........................................................................8
3.1.3. Norm ........................................................................................................9
3.1.4. Inner product and angle ...........................................................................9
3.2. Matrix............................................................................................................10
3.3. Determinant, Transpose and Inverse.............................................................103.4. Diagonal Matrices and Diagonal of a Matrix................................................10
3.5. Eigenvalues and Eigenvectors.......................................................................10
3.5.1. Householder Tridiagonalization and QR Factorization Methods..........10
3.5.2. Transformation to Hessenberg Form (Nonsymmetric Matrices)...........10
4. Finding Roots of Single Variable Equations .......................................................114.1. Bracketing Methods ......................................................................................11
4.1.1. Bisection Method ...................................................................................11
4.2. Open Methods...............................................................................................11
4.2.1. Fixed-Point Method ...............................................................................11
4.2.2. Newton’s Method (Newton-Raphson Method) .....................................11
4.2.3. Secant Method .......................................................................................11
4.2.4. Brent’s Method ......................................................................................11
5. Finding Roots of Systems of Equations...............................................................12
5.1. Linear Systems of Equations.........................................................................12
5.2. Gauss Elimination Method............................................................................12
5.3. LU Factorization Methods ............................................................................12
5.3.1. Cholesky Factorization ..........................................................................12
5.4. Iterative Solution of Linear Systems.............................................................12
5.5. System of Nonlinear Equations.....................................................................126. Curve Fitting and Interpolation............................................................................14
6.1. Least-Squares Regression .............................................................................14
6.2. Linear Regression..........................................................................................14
6.3. Polynomial Regression..................................................................................14
6.4. Polynomial Interpolation...............................................................................14
6.5. Spline Interpolation .......................................................................................14
7. Numerical Differentiation and Integration...........................................................15
7.1. Numerical Differentiation .............................................................................15
7.2. Finite-Difference Formulas...........................................................................15
7.3. Newton-Cotes Formulas................................................................................15
7.3.1. Rectangular Rule....................................................................................15
7.3.2. Trapezoidal Rule....................................................................................15
7.3.3. Simpson’s Rules.....................................................................................15
7.3.4. Higher-Order Newton-Coles Formulas..................................................15
7.4. Romberg Integration .....................................................................................15
7.4.1. Gaussian Quadrature..............................................................................15
7.4.2. Improper Integrals..................................................................................15
8. Numerical Solution of Initial-Value Problems....................................................16
8.1. One-Step Methods.........................................................................................16
8.2. Euler’s Method..............................................................................................16
8.3. Runge-Kutta Methods...................................................................................16
8.4. Systems of Ordinary Differential Equations.................................................16
9. Numerical Solution of Partial Differential Equations..........................................17
9.1. Elliptic Partial Differential Equations...........................................................17
9.1.1. Dirichlet Problem...................................................................................17
9.2. Parabolic Partial Differential Equations........................................................17
9.2.1. Finite-Difference Method ......................................................................17
9.2.2. Crank-Nicolson Method.........................................................................17
9.3. Hyperbolic Partial Differential Equations.....................................................17
10..................................................................................................................................18
11..................................................................................................................................19
12. Random Numbers and Simulation ....................................................................20
12.1. Uniform Distribution .................................................................................20
12.2. Normal Distribution...................................................................................20
12.3. Exponential Distribution............................................................................20
12.4. Poisson Distribution ..................................................................................20
12.5. Beta Distribution........................................................................................2012.6. Gamma Distribution ..................................................................................20
12.7. Multi-dimension Distribution ....................................................................20
13. Unconstrainted Optimization ............................................................................21
13.1. Single Variable Optimization ....................................................................21
13.2. Multi Variable Optimization .....................................................................21
14. Constrained Optimization .................................................................................22
14.1. Linear Programming..................................................................................22
14.2. Quadratic Programming ............................................................................22
14.3. Second Order Conic Programming............................................................22
14.4. Sequential Quadratic Programming...........................................................22
14.5. Integer Programming.................................................................................22
15. Heuristic Optimization......................................................................................23
15.1. Genetic Algorithm .....................................................................................23
15.2. Simulated Annealing .................................................................................23
16. Basic Statistics..................................................................................................24
16.1. Mean, Variance and Covariance................................................................24
16.2. Moment......................................................................................................24
16.3. Rank...........................................................................................................24
17. Linear Regression .............................................................................................25
17.1. Least-Squares Regression..........................................................................25
17.2. General Linear Least Squares....................................................................25
18. Time Series Analysis ........................................................................................26
18.1. Univariate Time Series..............................................................................2618.2. Multivariate Time Series ...........................................................................26
18.3. ARMA .......................................................................................................26
18.4. GARCH .....................................................................................................26
18.5. Cointegration .............................................................................................26
19. Bibliography .....................................................................................................27
20. Index .....................................................................................................
