Numerical Analysis and Optimization


At the end of this course the student will have acquired knowledge and skills that will enable him:

(i) to approximate the solution of ill-conditioned linear systems;

(ii) to approximate the first and higher order derivatives of a function;

(iii) to approximate the solution of initial value problems;

(iv) to numerically solve some unconstrained nonlinear optimization problems.

Furthermore,the student should be able to implement, using a computational language, the algorithms related with the covered numerical methods and analyze the numerical results obtained.

General characterization





Responsible teacher

Magda Stela de Jesus Rebelo


Weekly - 4

Total - 52

Teaching language



Available soon


1. R. Burden, D. Faires, Numerical Analysis, 9th edition, Brooks-Cole Publishing, 2011.

2. I. Griva, S. G. Nash, A. Sofer, Linear and Nonlinear Optimization, second edition, SIAM, 2009.

3. R. Kress, Numerical Analysis, Graduate Texts in Mathematics 181, Springer, 1998.

4. J. Nocedal, S. Wright, Numerical Optimization, second edition, Springer, 2006.

Teaching method

Available soon

Evaluation method

Available soon

Subject matter

1. Numerical Differentiation: derivatives of first order (forward, backward and central difference formulas), higher order derivatives. Richardson''s extrapolation.

2. Unconstrained Nonlinear Optimization methods: optimality conditions, line-search methods (steepest descent, Newton’s method, quasi-Newton’s methods), linear conjugate gradient method.

3. Complements of Numerical Linear Algebra numerical solution of ill-conditioned linear systems: singular value decomposition methods, Tikhonov regularization method.

4. Initial Value Problems for ODEs: one-step methods, explicit and implicit multistep methods, predictorcorrector methods.