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Numerical linear algebra 2

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Course Unit Code470-2211/03
Number of ECTS Credits Allocated3 ECTS credits
Type of Course Unit *Compulsory
Level of Course Unit *First Cycle
Year of Study *Second Year
Semester when the Course Unit is deliveredWinter Semester
Mode of DeliveryFace-to-face
Language of InstructionCzech
Prerequisites and Co-Requisites Course succeeds to compulsory courses of previous semester
Name of Lecturer(s)Personal IDName
HOR33doc. Ing. David Horák, Ph.D.
Summary
The subject's core consists in effiecient parallel linear algebra algorithms exploiting fully the computational power of nowadays supercomputers.
Learning Outcomes of the Course Unit
Linear algebra is behind the solution of large-scale engineering problems. In Numerical linear algebra 2 students get familiar with modern software libraries with efficient sequential and parallel implementations of linear algebra algorithms and with their applications.
Course Contents
Outline:
1. Numerical libraries overview
2. Basic operations with parallel objects in PETSc - vectors, matrices, index sets
3. Direct solvers and their parallelization - multifrontal vs. supernodal methods
4. Iterative solvers in PETSc - KSP
5. Spectral analysis using SLEPc
6. Preconditioning
Recommended or Required Reading
Required Reading:
- G. H. Golub, C. F. Van Loan - Matrix computations. Johns Hopkins University Press, 2012.
- PETSc Users Manual, http://www.mcs.anl.gov/petsc/petsc-current/docs/manual.pdf
- Z. Dostál, V. Vondrák - Lineární algebra. Skripta VŠB-TU Ostrava, http://mi21.vsb.cz, 2012.

Recommended Reading:
- Y. Saad - Iterative methods for sparse linear systems. SIAM, 2003.
- J.D. Tebbens, I. Hnětynková, M. Plešinger, Z. Strakoš, P. Tichý - Analysis of Methods for Matrix Computations. Basic Methods. Matfyzpress Prague, 2012.
Planned learning activities and teaching methods
Tutorials, Project work
Assesment methods and criteria
Task TitleTask TypeMaximum Number of Points
(Act. for Subtasks)
Minimum Number of Points for Task Passing
CreditCredit100 51