The notes are taken from the books required for the course:
📚 Course Syllabus
According to the official course syllabus:
Lectures will cover the following topics:
- Iterative methods for large linear systems:
- Sparse matrix storage formats;
- Krylov subspace iterative methods (CG, GMRES, BiCG, BiCGstab, ...);
- HPC programming and implementation of iterative solvers;
- Domain decomposition preconditioners: non-overlapping and overlapping techniques;
- (Algebraic) multigrid/multilevel methods.
- Direct methods for sparse linear systems:
- Graph reordering and fill-in;
- Graph partitioning and parallelization;
- The multifrontal method.
- Numerical algorithms for Machine Learning:
- Least square approximations;
- Numerical techniques for QR factorization;
- (L)-BFGS (hints).
- Numerical approximation of eigenvalues:
- Lanczos methods;
- Numerical algorithms based on approximate factorizations.
Computer Labs. The Computer Lab sessions are based the parallel software library LIS (Library of Iterative Solvers for linear systems). A quick overview of HPC linear algebra libraries such as Eigen, MUMPS, Lapack will also be covered.
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