Syllabus
1. Basic terminology from computers, factorizzations and computational complexity.
2. Direct methods, their representation by graphs and sparse matrices in applications.
3. Graph interpretation of Cholesky factorization and LU decomposition. Theoretical basis and algorithmic synthesis of sparse direct solvers.
4. Direct and approximate methods. The use of approximate decompositions in preconditioning. Sparse QR decomposition. Sparse decompositions of symmetric indefinite systems.
5. Implementations of direct and approximate solvers. The exam will test basic understanding to the subject described in this sylabus. The exam can preceed getting credits. The credits will be given based on the student activity. In order to ge the credits, at least one talk based on an independent work offered by the lecturer should be given.
Annotation
The goal of this course is to present contemporary algorithms and techniques dealing with sparse matrices for solving large and sparse systems of linear equations. Such systems arise in many practical problems of mathematical modeling, for example as a result of discretizations of partial differential equations as well as in applications in such diverse fields as management science, economy or chemical and biological sciences.