Lecture 12

29 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

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Systems of linear and non-linear equations: the Gauss-Seidel method to solve linear systems; convergence properties of general matrix iteration methods; systems of non-linear equations; the gradient matrix; Newton's method and its convergence properties.

Lecture 11

29 Setembro 2026, 17:30 • Jorge Miguel Cruz Pereira Varelas da Rocha

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Systems of linear and non-linear equations: results about matrix norms and their relation with the spectral radius; general matrix iteration methods; the Jacobi method to solve linear systems; implementation of Jacobi's method in MATLAB.

Lecture 10

25 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

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Systems of linear and non-linear equations: introduction; the spectrum and spectral radius of a square matrix; normed vector spaces; relation between norms and distances; matrix norms; the induced norm; the Frobenius norm.

Lecture 9

25 Setembro 2026, 17:30 • Jorge Miguel Cruz Pereira Varelas da Rocha

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Systems of linear and non-linear equations: introduction; review of linear algebra, highlighting the need to consider complex-valued matrices, eigenvectors and eigenvalues. Fully worked out example: computation of an arbitrary (integer) power of a 2x2 matrix.

Lecture 8

22 Setembro 2026, 19:00 • Jorge Miguel Cruz Pereira Varelas da Rocha

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Numerical solutions of algebraic equations in one variable: fixed point iterations and their convergence; Newton(-Raphson) method; the secant method; rates of convergence.