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| NMAC15 | Numerical linear algebra and optimization, 5 p (sw) /Numerisk lineär algebra och optimering/ Advancement level: C | |
| Aim: To give an overview of numerical methods for the solution of problems in numerical linear algebra and unconstrained optimization and to prevent the theory needed to analyze the methods. To give practical experience of the methods through computer experiments. Prerequisites: Knowledge of mathematics and numerical analysis as taught in the first two years of the mathematics program.Supplementary courses: NMAC16 Numerical solution of differential equationsCourse organization: The course consists of lectures, lessons and computer exercises.Course content: Linear algebra: Norms. Partitioning and block matrices. Givens transformation. Householder transformation. QR-factorization. The singular value decomposition. Symmetric, positive definite matrices. Iterative methods for the solution of systems of linear equations. Linear least squares problems. The matrix eigenvalue problem. Nonlinear unconstrained optimization: Newton-like methods. Conjugate gradient methods. Trustregion methods. Non-linear least squares problems. Course literature: Dahlquist-Björck: Numerical methods, Ch. 6, 7, 10-12. Exercises and examples of earlier written examinations. | ||
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