To show the organization of the course that includes this module, follow this link Course organization
Implementation in Matlab and/or GNU Octave of the main algorithms of numerical analysis.
* Error analysis.
Overflow, underflow, cancellation errors.
* Non-linear equations.
Bisection method. Fixed point iteration. Secant method, Newton's method and Aitken's acceleration. Polynomials: Horner's scheme.
* Linear systems.
Direct methods: LU factorization and pivoting, backward and forward substitutions.
Iterative methods: Jacobi's method, Gauss-Seidel's method and SOR. Iterative refinement. Richardson's method and gradient method. Sparse systems. Over- and underdetermined systems.
* Eigenvalues and eigenvectors.
Eigenvalue localization: Gershgorin's disks. Power method and inverse power method, QR. Eigenvalues of tridiagonal matrices: Schur's technique.
* Function interpolation and approximation.
Polunomial interpolation: Lagrange's and Newton's representation. Approximation error estimate. Trigonometric interpolation and Fast Fourier Transform. Piecewise polynomials interpolation and "splines". Least squares and
* Numerical differentiation and integration
Simple derivative approximation formulas.
Quadrature: simple and composite interpolation formulas. Quadrature error. Adaptivity. Gaussian formulas.
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