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12773 Numerical Approximation - Five-year degree in Mathematics

Center

Faculty of Mathematics

Departament

Applied Mathematics

Lecturers in charge

F1061 - JOSE VICENTE ARNAU CORDOBA

Met. Docent

Met. Avaluació

- -

Bibliografia

1.- S. Amat, F. Aràndiga, J.V. Arnau, R. Donat, P. Mulet & R. Peris, "Aproximació Numèrica", Universitat de València, España, 2003.
2.- A. Aubanell, A. Benseny & A. Delshams, "Eines Bàsiques de Càlcul Numèric", Manuals de la Universitat Autonoma de Barcelona, España, 1991.
3.- R. Burden & J. Faires, "Análisis Numérico", Grupo Editorial Iberoamericano, México, 1985.
4.- S. Conte & C. de Boor, "Análisis Numérico", McGraw Hill, México, D.F., seg. ed. 1974.
5.- G. Dalhquist & A. Bj÷rck, "Numerical Methods", PrenticeHall, Englewood Cliffs, NJ, 1974.
6.- G. Forsythe, M. Malcolm & C. Moler, "Computer Methods for Mathematical Computations", PrenticeHalls, Englewood Cliffs, NJ, 1977.
7.- R. Hamming, "Numerical Methods for Scientists and Engineers", McGrawHill, México, D.F.,

Continguts

Objectives
Before a concrete problem, the numerical analyst looks for solutions. It is important to assure that the problem to solve has a unique solution, but it is also important to calculate an approximation and it is necessary to find a bench mark of this approximation error.

Theory Programme
1. - Numerical systems and sources of error.
2. - Non linear equations.
3. - Analysis of convergence.
4. - Polynomial Equations.
5. - Functional approximation
6. - Lagrange interpolation problem.
7. - Election of interpolation nodes.
8. - Hermite interpolation problem.
9. - Segmental polynomial interpolation
10. - Approximation in normative spaces .
11. - Continuous approximation of square minima.
12. - Discrete square minima: the problem of data adjustment

Practical Programme
1. - Introduction to the MATLAB. Algorithms of base change for integers and fractions. Numerical experimentation with floating point arithmetics and its limits.Examples of numeric instability.
2. - Numerical experimentation in the calculation of solutions to non-linear equations with the different methods studied in theory. Order and speed of convergence.
3. - Iteration of fixed point, election of the function g(x). Order and speed. Numeric confirmation. Demarcation of polynomial roots. Multiple roots and deflaction.
4. - Interpolation with Taylor, Lagran