Course Outline
Numerical Analysis
NUMERICAL ANALYSIS
Polynomial approximation
- Interpolation by polynomials. Divided differences of functions and relations to derivatives. Orthogonal polynomials and their recurrence relations. Least squares approximation by polynomials. Gaussian quadrature formulae. Peano kernel theorem and applications. [6]
Computation of ordinary differential equations
- Euler’s method and proof of convergence. Multistep methods, including order, the root condition and the concept of convergence. Runge-Kutta schemes. Stiff equations and A-stability. [5]
Systems of equations and least squares calculations
- LU triangular factorization of matrices. Relation to Gaussian elimination. Column pivoting. Factorizations of symmetric and band matrices. The Newton-Raphson method for systems of non-linear algebraic equations. QR factorization of rectangular matrices by Gram–Schmidt, Givens and Householder techniques. Application to linear least squares calculations. [5]
Appropriate books
- † S.D. Conte and C. de Boor Elementary Numerical Analysis: an algorithmic approach. McGraw–Hill 1980
- G.H. Golub and C. Van Loan Matrix Computations. Johns Hopkins University Press 1996
- A Iserles A first course in the Numerical Analysis of Differential Equations. CUP 2009
- E. Suli and D.F. Meyers An introduction to numerical analysis. CUP 2003
- A. Ralston and P. Rabinowitz A first course in numerical analysis. Dover 2001
- M.J.D. Powell Approximation Theory and Methods. CUP 1981 P.J. Davis Interpolation and Approximation. Dover 1975
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