Valeria Simoncini (Università di Bologna)

Advanced Numerical Analysis

1. General considerations on matrices
Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)

2.a Direct methods for general linear systems
Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability

Advanced Numerical Analysis

1. General considerations on matrices

Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)


2.a Direct methods for general linear systems

Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability


2.b Direct methods for sparse linear systems

Factorizations of banded matrices

Advanced Numerical Analysis

1. General considerations on matrices

Matrices:definitions and properties; norm of matrices
The condition number of a matrix
Sparse matrices and sparse formats (sparsity, structure, functionals)
The role of the PDE discretization (e.g., parameter dependence)


2.a Direct methods for general linear systems

Factorizations: definitions and properties
Factorization algorithms
Cost and numerical stability


2.b Direct methods for sparse linear systems

Factorizations of banded matrices