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

Abschnittsübersicht

- Aktivität 2025-02-27: Introduction. Vectorization, Kronecker product. Sylvester equations; the Bartels-Stewart algorithm. auswählen
  
  2025-02-27: Introduction. Vectorization, Kronecker product. Sylvester equations; the Bartels-Stewart algorithm. Datei PDF
  
  4.5 MB
- Aktivität sylv triangular auswählen
  
  sylv triangular Datei M
  
  337 Bytes
- Aktivität 2025-02-28: conditioning of Sylvester equations, stability of the Bartels-Stewart algorithm auswählen
  
  2025-02-28: conditioning of Sylvester equations, stability of the Bartels-Stewart algorithm Datei PDF
  
  726.6 KB
- Aktivität 2025-03-06: Invariant subspaces. Definition and examples. Computing invariant subspaces by reordering Schur forms. auswählen
  
  2025-03-06: Invariant subspaces. Definition and examples. Computing invariant subspaces by reordering Schur forms. Datei PDF
  
  4.6 MB
- Aktivität 2025-03-07: Sensitivity of invariant subspaces; the Stewart-Sun theorem. Evaluating polynomials in a matrix in Jordan form; definition of functions of matrices. auswählen
  
  2025-03-07: Sensitivity of invariant subspaces; the Stewart-Sun theorem. Evaluating polynomials in a matrix in Jordan form; definition of functions of matrices. Datei PDF
  
  6.3 MB
- Aktivität 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. auswählen
  
  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. Datei PDF
  
  4.5 MB
- Aktivität 2025-03-20: more properties of matrix function. Convergence of Taylor expansions. Cauchy's integral formula. Fréchet derivatives with examples. auswählen
  
  2025-03-20: more properties of matrix function. Convergence of Taylor expansions. Cauchy's integral formula. Fréchet derivatives with examples. Datei PDF
  
  4.6 MB
- Aktivität 2025-03-21: block formula for the Fréchet derivative. Eigenvalues of Fréchet derivatives. auswählen
  
  2025-03-21: block formula for the Fréchet derivative. Eigenvalues of Fréchet derivatives. Datei PDF
  
  6.3 MB
- Aktivität 2025-03-27: example of low accuracy using Taylor series. The Parlett recurrence. The (blocked) Schur-Parlett method and funm. auswählen
  
  2025-03-27: example of low accuracy using Taylor series. The Parlett recurrence. The (blocked) Schur-Parlett method and funm. Datei PDF
  
  421.5 KB
- Aktivität funm parlett auswählen
  
  funm parlett Datei M
  
  298 Bytes
- Aktivität 2025-03-28: automatic differentiation: the main ideas through matrix functions, Taylor expansions. Some quick remarks on the multivariate case and reverse mode. auswählen
  
  2025-03-28: automatic differentiation: the main ideas through matrix functions, Taylor expansions. Some quick remarks on the multivariate case and reverse mode. Datei PDF
  
  4.5 MB
- Aktivität Taylor auswählen
  
  Taylor Datei M
  
  947 Bytes
- Aktivität 2025-04-03: the matrix exponential: properties; backward stability of Padé approximants; scaling and squaring. auswählen
  
  2025-04-03: the matrix exponential: properties; backward stability of Padé approximants; scaling and squaring. Datei PDF
  
  2.6 MB
- Aktivität 2025-04-04: the matrix sign function. Schur-Parlett method; the Newton iteration for the matrix sign: scalar version and convergence. auswählen
  
  2025-04-04: the matrix sign function. Schur-Parlett method; the Newton iteration for the matrix sign: scalar version and convergence. Datei PDF
  
  2.7 MB
- Aktivität 2025-04-10: numerical experiments with the matrix sign. Scaling. The matrix square root: Schur-Parlett variant, Newton iteration, modified Newton method. auswählen
  
  2025-04-10: numerical experiments with the matrix sign. Scaling. The matrix square root: Schur-Parlett variant, Newton iteration, modified Newton method. Datei PDF
  
  4.5 MB
- Aktivität 2025-04-11: (non-)convergence of the Newton method for the matrix square root. Variants. Functions of large and sparse matrices: general strategies, the Arnoldi approximation for matrix functions. auswählen
  
  2025-04-11: (non-)convergence of the Newton method for the matrix square root. Variants. Functions of large and sparse matrices: general strategies, the Arnoldi approximation for matrix functions. Datei PDF
  
  4.7 MB
- Aktivität 2025-04-17: Arnoldi for matrix functions: error bound for normal matrices. Brief overview of other recent results: numerical radius, Crouzeix-Palencia, and results for non-normal A; shift-and-invert Arnoldi and rational Arnoldi. auswählen
  
  2025-04-17: Arnoldi for matrix functions: error bound for normal matrices. Brief overview of other recent results: numerical radius, Crouzeix-Palencia, and results for non-normal A; shift-and-invert Arnoldi and rational Arnoldi. Datei PDF
  
  572.2 KB
- Aktivität 2025-05-02: Lyapunov and Stein equations. Introduction to control theory: the inverted pendulum auswählen
  
  2025-05-02: Lyapunov and Stein equations. Introduction to control theory: the inverted pendulum Datei PDF
  
  4.4 MB
- Aktivität 2025-05-07: example: heating. Controllability; definition and criteria. auswählen
  
  2025-05-07: example: heating. Controllability; definition and criteria. Datei PDF
  
  4.8 MB
- Aktivität 2025-05-15: Matlab examples of control systems. Linear-quadratic optimal control: the optimality theorem and the Riccati equation. auswählen
  
  2025-05-15: Matlab examples of control systems. Linear-quadratic optimal control: the optimality theorem and the Riccati equation. Datei PDF
  
  4.5 MB
- Aktivität 2025-05-16: Algebraic Riccati equations: equivalence to invariant subspace; structural properties of Hamiltonian matrices; existence of the stable invariant subspace and of the stabilizing Riccati solution. auswählen
  
  2025-05-16: Algebraic Riccati equations: equivalence to invariant subspace; structural properties of Hamiltonian matrices; existence of the stable invariant subspace and of the stabilizing Riccati solution. Datei PDF
  
  8.3 MB
- Aktivität CAREX benchmark suite auswählen
  
  CAREX benchmark suite Link/URL
  
  Link per scaricare il pacchetto Matlab con esempi di equazioni di Riccati che abbiamo usato nei nostri esempi
- Aktivität 2025-05-22: Methods for dense algebraic Riccati equations: Newton method; matrix-sign method; the Schur method. The importance of preserving the Hamiltonian structure. auswählen
  
  2025-05-22: Methods for dense algebraic Riccati equations: Newton method; matrix-sign method; the Schur method. The importance of preserving the Hamiltonian structure. Datei PDF
  
  8.1 MB
- Aktivität 2025-05-23: Methods for sparse Lyapunov equations: the ADI algorithm. Quick remarks on the pole selection problems and on rational Arnoldi. auswählen
  
  2025-05-23: Methods for sparse Lyapunov equations: the ADI algorithm. Quick remarks on the pole selection problems and on rational Arnoldi. Datei PDF
  
  6.5 MB