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

Events

  • Representations of fundamental groups of surfaces
    Peter Gothen (CMUP)
    15:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • On the existence of solutions for inextensible string equations
    Ayk Telciyan (student)
    12:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • Boolean representable simplicial complexes
    Maria Inês Couto (student)
    12:00, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • Campanato spaces and applications in partial differential equations
    David Jesus (student)
    11:30, Room 2.5, UC Math. Dept.
    (Seminar)
    November 23, 2018
  • A mathematical model for a plant circadian oscillator
    Adérito Araújo (CMUC)
    14:00, Room 2.5, UC Math. Dept.
    (Seminar)
    November 28, 2018
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Defended Theses

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