basic numerical analysis algorithms implemented in MATLAB for coursework.
- norm
- vector norm (p,+inf,-inf)
- matrix norm (1,2,inf,'fro')
- condition number
- rank
- QR
- SVD
- Gaussian elimination
- without pivoting
- with partial pivoting
- with complete pivoting
- Thomas method
- LU (Doolittle) decomposition
- with partial pivoting
- with complete pivoting
- decomposition for symmetric positive definite matrix
- Cholesky decomposition
- LDL decomposition
- QR decomposition
- Gram-Schimidt orthogonalization
- Givens transformation
- Householder transformation
- column pivoting
- Newton iteration
- Gauss-Jordan method with complete pivoting
- triangle inverse
- QR decomposition
- SVD (Pseudo Inverse)
- LU decomposition
- Jacobi iterative method
- Gauss-Seidel iterative method
- succesise over - relaxation method
- SOR
- symmetric SOR
- Krylov methods
- CG
- CGNE
- CGNR
- GMRES
- MINRES
- SYMMLQ
- QMR
- BiCG
- CGS
- BiCGstab
- LSQR
- preconditioning
- bisection method
- Steffensen acceleration for fixed-point iteration
- Newton method
- secant method
- Brent method
- Muller method
- Newton method
- Broyden method
- homotopy continuation method
- solving nonlinear LS problem
- Horner method
- finding roots using deflation
- finding roots using QR iteration
- Hessenberg
- bidiagonal
- tridiagonal
- power iteration
- inverse iteration (with shift)
- Rayleigh quotient iteration
- Jacobi method
- single shift
- double shift
- symmetric
- eigenvalue
- eigenpair of symmetric matrix
- deflation method
- matrix balance
- singular value decomposition
- polynomial interpolation
- Lagrange polynomial
- Newton polynomial
- Neville algorithm
- Hermite interpolation
- Lagrange polynomial
- Newton polynomial
- Chebyshev interpolation
- nearest interpolation
- linear interpolation
- cubic spline interpolation
- natural end conditions
- not-a-knot end conditions
- nearest interpolation
- linear interpolation
- Legendre
- Laguerre
- Hermite
- Chebyshev
- full rank least square
- normal equation
- QR
- SVD
- rank deficient least square
- QR
- SVD
- weighted least square
- Tikhonov regularization
- polynomial fit
- base 2
- base 3
- trapezoid
- Simpson
- Gaussian quadrature
- Gauss-Legendre
- Gauss-Chebyshev
- Gauss-Hermite
- Gauss-Laguerre
- Romberg
- Runge - Kutta method
- classic
- embedded
- implicit
- Linear multistep method
- Adams methods
- implicit Adams methods
- Adams-Bashforth four-step method with predictor-corrector
- Poisson equation
- heat equation
- wave equation
- Gauss-Newton
- Levenberg-Marquardt
- Nelder - Mead
- Runge phenomenon
- minimize error of polynomial interpolation using Chebyshev interpolation
- optimal relaxation factor for SOR
- round-off error in numerical differentiation
- common orthogonal polynomials
- Chebyshev acceleration in linear iteration
- Gershgorin disc theorem
- 数值分析基础(第二版),关治,陆金甫. Fundamentals of Numerical Analysis (Second Edition), Zhi Guan, Jinfu Lu.
- Numerical Analysis, Rainer Kress
- An Introduction to Numerical Analysis, Endre suli and David F. Mayers
- Applied Numerical Linear Algebra, James W. Demmel
- Numerical Analysis (2nd edition), Timothy Sauer
- Numerical Analysis (9th edition), Richard L. Burden, J. Douglas Faires
- Matrix Computation (4th edition), Gene H. Golub, Charles F. Van Loan
- Numerical Optimization (2nd edition), Jorge Nocedal, Stephen J. Wright