The first call for applications for the new edition of the PhD Program in Mathematics UC|UP (starting September 2019) will be open during January 02, 2019 - February 04, 2019
The prize Eng. António de Almeida for the best doctoral thesis defended at FCUP in the years 2015 to 2017 in the areas of Mathematics, Statistics and Computer Science was awarded to Célia Borlido for her thesis "The word problem and some reducibility properties for pseudo- varieties of the form DRH", supervised by Prof. Jorge Almeida within the scope of PIUDM.
Introduction. Matrix decompositions. Conditioning and stability. Floating point arithmetic. Error analysis.
Systems of equations. Gaussian elimination with pivoting strategies. Cholesky factorization. Stability analysis. Large systems of equations. Sparse matrix techniques. Iterative methods based on Krylov subspaces: Conjugate Gradients, GMRES, Biorthogonalization methods (BiCG and BICGstab). Convergence and spectral properties. Preconditioning.
Eigenvalues. Reduction to Hessenberg or tridiagonal forms. Rayleigh quotient and inverse iteration. QR algorithm. Lanczos iteration (symmetric case) and Arnoldi iteration (non symmetric case).