| Center |
| Faculty of Mathematics |
| Departament |
| Applied Mathematics |
| Lecturers in charge |
| G9278 - VICENTE JAVIER PASTOR MURCIA |
| Met. Docent |
| Met. Avaluació |
| Theoretical and practical tests. |
| Bibliografia |
| 1-Arandiga,F; Donat,R; Mulet, P. "Mètodes numèrics per a l'àlgebra lineal". Universitat de València. 2000. 2-Aubanell, A; Benseny,A.; Delshams, I;"Eines bàsiques de càlcul numèric". Manuals de la Universitat Autònoma de Barcelona. 1991. 3-Ciarlet,P.,"Introduction à l'Analyse Numérique Matricielle et a l'Optimisation". Masson, París. 1985. 4-Golub,G; Van Loan,C.; "Matrix Computations". Jonhs Hopkins University Press. 1989. 5-Ralston,A.;Rabinowitz,P.,"A First Course in Numerical Analysis".Dover.2001. |
| Continguts |
| Theory Programme 1-Introduction. Vector and matrix norms. Terminology. Eigenvalues and eigenvectors: spectral radius. 2-Linear systems and their numerical solution. Sensitivity to input perturbation of linear equations. 3-Direct methods. The Gaussian elimination. Partial and complete pivoting. 4-The LU factoritation. 5-Special systems. Systems with symmetric and positive definite matrix. 6-Iterative methods for linear systems. The standar iterations: Jacobi, Gauss-Seidel and successive over-relaxation. 7-Overdetermined linear systems. Least squares problem. 8-Methods for determining the eigenvalues and eigenvectors. The power and the inverse power methods. Practical Programme 1-Matlab nomenclature for matrices. Special matrices. 2-Numerical tests to analyse the sensitivity to input perturbation of linear equations. Practical estimate of the condition number of a matrix. 3-Practical implementation of direct methods to solve Ax=b. Solution of triangular systems. The LU decomposition. Practical estimate of error in gaussian elimination. 4-Programming iterative methods to solve Ax=b. Analysis of convergence properties. 5-Practical implementation of algorithms to estimate the eigenvalue with maximum modulus by means of the power method. Computation of the eigenvectors associated to an eigenvalue. |
| Objetius |
| Numerical lineal algebra deals with the obtaining of the solution of linear algebra problems. We focus our attention in the solution of systems of linear equations and the eigenvalue problem, by introducing and analysing suitable algorithms. The student will implement the algoritmths in order to use them in practical problems. |
| URL de Fitxa |