Numerical Methods of Linear Algebra
A tantárgyleírás hatályossága
| Subject name (Hungarian, English) |
A lineáris algebra numerikus módszerei
Numerical Methods of Linear Algebra
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| Subject code | BMEVIMAD041 | ||||||||||||
| Subject type | — | ||||||||||||
| Training Level | — | ||||||||||||
| Course types and hours (weekly/semester) |
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| Assessment type | vizsga | ||||||||||||
| Credits | 5 | ||||||||||||
| Subject coordinator |
Pach Péter Pál
contact:
pach.peter@vik.bme.hu
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| Responsible department |
Gépjárműtechnológia Tanszék
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| Faculty | Közlekedésmérnöki és Járműmérnöki Kar | ||||||||||||
| Subject website | http://cs.bme.hu/lanm | ||||||||||||
| Primary curriculum type | — | ||||||||||||
| Direct prerequisites – Strong prerequisite | none | ||||||||||||
| Direct prerequisites – Weak prerequisite | none | ||||||||||||
| Direct prerequisites – Parallel prerequisite | none | ||||||||||||
| Direct prerequisites – Milestone prerequisite | none | ||||||||||||
| Direct prerequisites – Exclusion | none |
Objectives
1) Vector and matrix norms, applications to
some important estimates, Rayleigh quotient.
2) Localisation of the
eigenvalues, Gershgorin circles.
3) Singular
values of a matrix. Singular value decomposition.
4) Moore-Penrose
pseudoinverse.
5) Linear equation systems,
condition number.
6) Numerical
solution of linear equation systems. Direct methods: Crout version of Gaussian
elimination.
7) Solving a
linear equation system when the coeffient matrix is tridiagonal.
8) Conjugate
gradient method.
9) Iterative methods: Gauss-Seidel method; Successive
over-relaxation. Alternating direction method.
10) Application: solving the Poisson equation. Tensor product.
11) Numerical solution
of the eigenvalue problem.
12) The
power iteration and the inverse iteration method, Mises theorem.
13) The eigenvalue problem of real symmetric matrices.
14) The Householder transformation .
15) The
eigenvalue problem for tridiagonal matrices, Sturm's theorem.
16) The
eigenvalue problem for nonsymmetric matrices.
17) Transformation
to Hessenberg form.
18) QR transformation.
19) Applications of
the Courant-Fischer theorem.
20) Lánczos method.
21) Different kind of applications depending on time and interest, e.g. numerical solutions of differential equations, cluster analysis, PageRank.
Learning outcomes
Ez a tantárgy a KKK rendeletben meghatározott, következő kompetenciák fejlesztését szolgálja:
Knowledge
No learning outcomes recorded.
Skills
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Attitudes
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Autonomy and responsibility
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Oktatási módszertan
Tanulástámogató anyagok
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Short description
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