Table of contents of this book:
Chapter 1 Solutions to Systems of Linear Algebraic Equations
1.Full pivot Gaussian Jordan elimination method
2.LU decomposition method
3.Catch-up method
4.Solution method of five diagonal linear equations
5. Iterative improvement of solutions to linear equations
6.Solution method of Vandermond’s equations
7.Solution method of Tobelitz equations
8. Singular value decomposition
9. Conjugate gradient method for linear equations
10. Choleski decomposition method of symmetrical equations
11. QR decomposition of matrix
12. Relaxation Iteration Method Chapter 2 Interpolation
1. Lagrangian interpolation
2. Rational function interpolation
3. Cubic spline interpolation
4. Search method of ordered list
5. Interpolation polynomial
6. Binary Lagrangian interpolation
7. Bicubic Spline Interpolation Chapter 3 Numerical Integration
1. Trapezoidal quadrature method
2. Simpson’s quadrature method
3. Romberg quadrature method
4.Abnormal integral
5. Gaussian quadrature method
6. Triple Integral Chapter 4 Special Functions
1.г function, beta function, factorial and binomial coefficient
2. Incomplete г function, error function
3. Incomplete beta function
4. Bessel functions of the first and second kinds of zeroth order, first order and any integer order
5. Deformed Bessel functions of the first and second types of zero order, first order and any integer order
6. Fractional Bessel functions of the first kind and deformed Bessel functions
7. Exponential integral and fixed exponential integral
8. Associated Legendre Function Chapter 5 Function Approximation
1.Series summation
2.Polynomials and rational functions
3. Chebyshev approaches
4. Chebyshev approximation of integrals and derivatives
5. Polynomial approximation of functions with Chebyshev approximation Chapter 6 Eigenvalue problem
1. Jacobian transformation of symmetric matrices
2. Convert the real symmetric matrix into a tridiagonally symmetric matrix
3. Eigenvalues and eigenvectors of tridiagonal matrices
4. Change the general matrix to the Hershenberg matrix
5. QR algorithm for real Hirschenberg matrix Chapter 7 Data Fitting
1. Straight line fitting
2. Linear least squares method
3. Nonlinear least squares method
4. Straight line fitting with minimum absolute value deviation Chapter 8 Equation root finding and solution of nonlinear equations
1. Graphical method
2. Stepwise scanning method and dichotomy method
3.Secant method and trial position method
4. Brent Method
5. Newton-Raphson method
6. Laguerre method for finding roots of polynomials with complex coefficients
7. Bairstow's method for finding the roots of polynomials with real coefficients
8. Newton-Lapheus Method for Nonlinear Equations Chapter 9 Extreme Values and Optimization of Functions
1. Golden section search method
2. Brent method without derivatives
3. Brent’s method using derivatives
4. Downhill simplex method for multivariate functions
5. Bauvier method for multivariate functions
6. Conjugate gradient method for multivariate functions
7. Variable scaling method for multivariate functions
8. Simplex Method for Linear Programming Chapter 10 Fourier Transform Spectral Method
1. Complex data fast Fourier transform algorithm
2. Real data fast Fourier transform algorithm 1
3. Real data fast Fourier transform algorithm 2
4. Fast sine transform and cosine transform
5. Fast algorithms for convolution and deconvolution
6. Fast algorithms for discrete correlation and autocorrelation
7. Multidimensional Fast Fourier Transform Algorithm Chapter 11 Statistical Description of Data
1. Moments of distribution - mean, mean deviation, standard deviation, variance, skew and kurtosis
2. Search for median
3. Significance test of mean and variance
4. X-squared test of distribution fitting
5. KS Test Method for Distribution Fitting Chapter 12 Solving Systems of Ordinary Differential Equations
1. Fixed step length fourth-order Runge-Kutta method
2. Runge-Kutta method with adaptive variable step size
3. Improved midpoint method
4. Extrapolation Method Chapter 13 Solution of Partial Differential Equations
1. Relaxation method for solving boundary value problems
2. Alternate direction implicit method
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