Numerical Linear Algebra


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).

Research and Events


  • PhD Defense
    Khadijeh Alibabaei - On the profinite topology on groups and tameness of pseudo-varieties of groups
    15h00m - Room FC1 029, Dep. Mathematics, Univ. Porto
    March 1, 2018
  • Research Seminar Program (RSP)
    2017/18 second session
    Room 2.5, DMat UC
    March 9, 2018
  • PhD Defense
    Muhammad Ali Khan - Statistical instability in chaotic dynamics
    Room 031, Dep. Mathematics, Univ. Porto
    March 9, 2018
  • PhD Defense
    Anderson Feitoza Leitão Maia - Sharp regularity for the inhomogeneous porous medium equation
    14:30 - Sala dos Capelos, Univ. Coimbra
    March 21, 2018
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Defended Theses

  • Forward-backward stochastic differential equations and applications
      Rui Manuel Tavares Pinto de Sá Pereira (January 2018)
      Evelina Shamarova
      Margarida Brito
  • Pseudomonads and descent
      Fernando Lucatelli Nunes (January 2018)
      Maria Manuel Clementino
  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
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