| Course title | Advanced Numerical Methods |
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| Course code | KI/EPNUM |
| Organizational form of instruction | Lecture + Lesson |
| Level of course | Master |
| Year of study | not specified |
| Semester | Winter |
| Number of ECTS credits | 8 |
| Language of instruction | English |
| Status of course | unspecified |
| Form of instruction | Face-to-face |
| Work placements | This is not an internship |
| Recommended optional programme components | None |
| Course availability | The course is available to visiting students |
| Lecturer(s) |
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| Course content |
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1. Sources of numerical errors, the numerical stability of algorithms 2-3. System of linear equations, conditional number, Gaussian elimination LU factorization, Cholesky and QR factorization 4-5. Iterative methods for the solution of linear algebraic equations: Jacobi method, Gauss-Seidel method, SOR, steepest descent method and conjugate gradient method. 6-7. Eigenvalues of the matrix: partial eigenvalues problem - power method, full eigenvalues problem QR iteration 8. Singular Value Decomposition - SVD: computation and applications 9. Method for nonlinear equations, Newton's (Newton-Rhapson) method, fixed point method, etc. 10. Root finding for polynomials, Horner scheme 11. Principles of numerical quadrature: Newton-Cotes rules, Romberg's quadrature method, Gaussian quadrature rules, MC and adaptive methods 12. Principles of numerical solution of ODEs: one-step methods, Runge-Kutta methods, stiff system, stability, etc. 13. Function interpolation and approximation: Lagrange interpolation, cubic spline interpolation, Chebychev approximation
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| Learning activities and teaching methods |
| unspecified |
| Learning outcomes |
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This course is an extension of the basic course of numerical methods with respect to numerical linear algebra and parts used in machine learning.
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| Prerequisites |
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Basics from linear algebra (vectors, matrices, vector spaces) and analysis and basic principles of numerical method
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| Assessment methods and criteria |
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unspecified
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| Recommended literature |
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| Study plans that include the course |
| Faculty | Study plan (Version) | Category of Branch/Specialization | Recommended semester |
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