PT EN

Numerical Linear Algebra

Program

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

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Defended Theses

  • Topic Summation and Transformation formulas related with Spectral Functions
      Pedro Manuel Macedo Ribeiro (January 2025)
      Semyon Yakubovich
  • Numerical methods for the robust reconstruction of elasticity
      Rafael Oliveira Henriques (January 2025)
      Sílvia Barbeiro
  •   Vincenzo Bianca (July 2024)
      José Miguel Urbano
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