Belépés címtáras azonosítással
magyar nyelvű adatlap
angol nyelvű adatlap
Numerical Methods of Linear Algebra
A tantárgy neve magyarul / Name of the subject in Hungarian: A lineáris algebra numerikus módszerei
Last updated: 2023. szeptember 6.
Dr. Friedl Katalin
associate professor
Department of Computer Science and Information Theory
Dr. Pach Péter Pál
Linear algebra, mathematical analysis.
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.
4 hours of lecture per week.
Signature: 1 homework.
Final: oral exam.
In office hours or by appointment.
Rózsa Pál: Lineáris algebra és alkalmazásai. 3. átdolgozott kiadás. Tankönyvkiadó, Budapest, 1991.
H. Golub – C.F. Van Loan: Matrix Computations, The John Hopkins University Press, 1989.
Dr. Rózsa Pál, professor, Department of Computer Science and Information Theory
