023_delphi common numerical algorithm set

Delphi common numerical algorithm set

DelphiTutorial Series of books(023)《DelphiCommon numerical algorithm set Organize netizens (state)Email:Shuaihj@163.com

:

PDF

• Author: He Guangyu leiqun
• Series name: commonly used numerical algorithm series
• Press: Science Press
• ISBN: 7030096991
• Mounting time: 2001-11-9
• Published on: February 1, September 2001
• Page number: 660
• Version: 1-1

Introduction

This book contains more than 100 commonly used Delphi subprocesses in numerical computation, the content includes linear algebra equations, interpolation, numerical integration, special functions, function approximation, feature value problems, data fitting, equation root and nonlinear equations, function extreme value and optimization, and data statistics. description, Fourier transform spectral method, solution of the ordinary differential equations, and partial differential equations. each process includes functions, methods, instructions, processes, and examples. all the sub-processes in this book are verified in Delphi 4.0, Which is accurate. the assignment is accompanied by an electronic version, including the Delphi project for all sub-processes.

This book can be used by college teachers, students, research institutes, engineering and technical personnel of industrial and mining enterprises.

Directory

Collation

Preface

Chapter 1 solutions to linear algebra equations

1.1 Gauss-Jordan elimination

1.2 Lu Decomposition Method

1.3 catch-up

1.4 solution to five diagonal Linear Equations

1.5 iterative improvement of Solutions to Linear Equations

1.6 solutions to the Van dermonde Equations

1.7 Toeplitz Equations

1.8 Singular Value Decomposition

1.9 Gradient Method for Linear Equations

1. Cholesky Decomposition of 10 symmetric Equations

1.11 matrix QR decomposition

1.12 relaxation Iteration Method

Chapter 2 interpolation

2.1 Laplace Interpolation

2.2 rational function interpolation

2.3 cubic spline interpolation

2.4 query method for ordered tables

2.5 Interpolation Polynomials

2.6 binary Laplace Interpolation

2.7 double Cubic Spline Interpolation

Chapter 2 numerical points

3. 1 trapezoid Product Method

3.2 Simpson (Simpson) Product Method

3.3 Romberg Product Method

3.4 abnormal points

3.5 Gaussian (Gauss) Product Method

3. 6 triple points

Chapter 4 Special Functions

4.1 function, beta function, factorial, and binary coefficient

4.2 incomplete functions and error functions

4.3 incomplete beta function

4.4 first-and second-class besell functions of the zero, first, and any integer order

4.5 The first and second class deformation functions of the zero, first, and any integer order

4.6 first class of score-level betel functions and transformed betel Functions

4.7 index points and fixed index points

4.8 join the role function

Chapter 1 Function Approximation

5.1 series summation

5.2 polynomials and rational functions

5.3 kibihov approaching

5.4 cut-over approximation of points and Derivatives

5.5 calculate polynomial approximation of a function by using cherbihov Approximation

Chapter 2 feature Value Problems

6. 1 KNN transformation of symmetric matrix

6. 2. Change the real symmetric matrix to a three-diagonal symmetric matrix.

6.3 feature values and feature vectors of the tridiagonal matrix

6.4 change the general matrix to the hershenberger Matrix

6.5 real-Herberger matrix QR Algorithm

Chapter 3 Data Fitting

7.1 straight line fitting

7.2 Linear Least Square Method

7.3 Nonlinear Least Square Method

7.4 linear fitting with the smallest absolute value Deviation

Appendix

Chapter 2 solutions to equations root and Nonlinear Equations

8.1 Graphic Solution

8.2 step-by-step scan method and binary method

8.3 cut line method and test position method

8.4 Brent (Brent) Method

8.5 Newton-laferson (Newton-Raphson) Method

8.6 Laguerre Method for Finding the complex polynomial Root

8.7 realistic factor polynomial Root's bear column (bairstou) Method

8.8 Newton-laferson Method for Nonlinear Equations

Chapter 1 extreme values and optimization of functions

9.1 golden segmentation search

9.2 Brent method without derivative

9.3 Brent method with Derivative

Simple down-hill form of 9.4 multivariate Functions

Packell (Powell) method of 9.5 multivariate Functions

9.6 multivariate function-based gradient method

Variable Scale Method for 9.7 multivariate Functions

9.8 simple shape method for Linear Planning

Chapter 2 Fourier transform Spectral Method

10.1 complex data fast Fourier Transformation Algorithm

10.2 real data fast Fourier transformation algorithm (I)

10.3 real data fast Fourier transformation algorithm (2)

10.4 fast sine transformation and cosine transformation

10. 5 Quick Algorithms for Convolution and inverse convolution

10.6 Fast Algorithms for discrete correlation and self correlation

10.7 multidimensional Fast Fourier Transform Algorithm

Chapter 3 statistical description of data

Moment of 11.1 distribution-mean, mean difference, standard deviation, variance, oblique difference and peak state

Search for the median of 11.2

11.3 mean and variance significance test

11.4 X2 test of distribution fitting

11.5 distributed fitting K-S Test Method

Chapter 2 solutions of Ordinary Differential Equations

12.1 fixed step-4 rank long-Kuta (Runge-Kutta) Method

12.2 adaptive Step-changing long Ge-Kuta method

12.3 improved midpoint method

12.4 external push Method

Chapter 1 solutions to partial differential equations

13.1 Relaxation Method for Solving edge Value Problems

13.2 alternating direction implicit method (ADI)

References

Post notes