Metodi di Approssimazione 2024 25, Sezione: Topic 1 | MAT - e-learning

Schema della sezione

- Seleziona attività 2025-02-27: Introduction. Vectorization, Kronecker product. Sylvester equations; the Bartels-Stewart algorithm.
  
  2025-02-27: Introduction. Vectorization, Kronecker product. Sylvester equations; the Bartels-Stewart algorithm. File PDF
  
  4.5 MB
- Seleziona attività sylv triangular
  
  sylv triangular File M
  
  337 bytes
- Seleziona attività 2025-02-28: conditioning of Sylvester equations, stability of the Bartels-Stewart algorithm
  
  2025-02-28: conditioning of Sylvester equations, stability of the Bartels-Stewart algorithm File PDF
  
  726.6 KB
- Seleziona attività 2025-03-06: Invariant subspaces. Definition and examples. Computing invariant subspaces by reordering Schur forms.
  
  2025-03-06: Invariant subspaces. Definition and examples. Computing invariant subspaces by reordering Schur forms. File PDF
  
  4.6 MB
- Seleziona attività 2025-03-07: Sensitivity of invariant subspaces; the Stewart-Sun theorem. Evaluating polynomials in a matrix in Jordan form; definition of functions of matrices.
  
  2025-03-07: Sensitivity of invariant subspaces; the Stewart-Sun theorem. Evaluating polynomials in a matrix in Jordan form; definition of functions of matrices. File PDF
  
  6.3 MB
- Seleziona attività 2025-03-13: Examples of matrix functions. Examples of multi-branch and non-primary functions. Some properties of matrix functions that descend from their expression as polynomials.
  
  2025-03-13: Examples of matrix functions. Examples of multi-branch and non-primary functions. Some properties of matrix functions that descend from their expression as polynomials. File PDF
  
  4.5 MB
- Seleziona attività 2025-03-20: more properties of matrix function. Convergence of Taylor expansions. Cauchy's integral formula. Fréchet derivatives with examples.
  
  2025-03-20: more properties of matrix function. Convergence of Taylor expansions. Cauchy's integral formula. Fréchet derivatives with examples. File PDF
  
  4.6 MB
- Seleziona attività 2025-03-21: block formula for the Fréchet derivative. Eigenvalues of Fréchet derivatives.
  
  2025-03-21: block formula for the Fréchet derivative. Eigenvalues of Fréchet derivatives. File PDF
  
  6.3 MB
- Seleziona attività 2025-03-27: example of low accuracy using Taylor series. The Parlett recurrence. The (blocked) Schur-Parlett method and funm.
  
  2025-03-27: example of low accuracy using Taylor series. The Parlett recurrence. The (blocked) Schur-Parlett method and funm. File PDF
  
  421.5 KB
- Seleziona attività 2025-03-28: automatic differentiation: the main ideas through matrix functions, Taylor expansions. Some quick remarks on the multivariate case and reverse mode.
  
  2025-03-28: automatic differentiation: the main ideas through matrix functions, Taylor expansions. Some quick remarks on the multivariate case and reverse mode. File PDF
  
  4.5 MB
- Seleziona attività 2025-04-03: the matrix exponential: properties; backward stability of Padé approximants; scaling and squaring.
  
  2025-04-03: the matrix exponential: properties; backward stability of Padé approximants; scaling and squaring. File PDF
  
  2.6 MB
- Seleziona attività 2025-04-04: the matrix sign function. Schur-Parlett method; the Newton iteration for the matrix sign: scalar version and convergence.
  
  2025-04-04: the matrix sign function. Schur-Parlett method; the Newton iteration for the matrix sign: scalar version and convergence. File PDF
  
  2.7 MB