470-2211/03 – Numerical linear algebra 2 (NLA2)
Gurantor department | Department of Applied Mathematics | Credits | 3 |
Subject guarantor | doc. Ing. David Horák, Ph.D. | Subject version guarantor | doc. Ing. David Horák, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 2 | Semester | winter |
| | Study language | Czech |
Year of introduction | 2020/2021 | Year of cancellation | |
Intended for the faculties | FEI | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
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.
Teaching methods
Tutorials
Project work
Summary
The subject's core consists in effiecient parallel linear algebra algorithms exploiting fully the computational power of nowadays supercomputers.
Compulsory literature:
- 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
Recommended literature:
- Y. Saad - Iterative methods for sparse linear systems. SIAM, 2003.
Way of continuous check of knowledge in the course of semester
Continuous study verification:
• Test - max. 60 points.
• Individual project on parallel implementation of chosen algorithm - max. 40 points.
Requirements for passing the subject:
• Writing the test.
• Submitting and successful defense of a project.
E-learning
Other requirements
Successful defense of a semestral project.
Students are familiar with fundamentals of linear algebra.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
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
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction