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The course is devoted to fundamentals of numerical linear algebra, with the concetration on methods for solving linear algebraic equations, including least squares, and on eigenvalue problems. The course builds upon the knowlegde of basic numerical methods (the course NNUM105), and emphasizes formulation of questions, motivation and interconnections.
Last update: T_KNM (22.05.2008)
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The course gives students a knowledge of fundamentals of numerical linear algebra with the concetration on methods for solving linear algebraic equations and on eigenvalue problems. Last update: T_KNM (17.05.2008)
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Watkins, D.S., Fundamentals of Matrix Computations (Second edition), J. Wiley & Sons, New York, 2002
Fiedler, M., Speciální matice a jejich užití. SNTL Praha, l980
Golub, G.H., Van Loan C.F., Matrix Computations (Third edition). J. Hopkins Univ. Press, Baltimore, 1996 Last update: T_KNM (17.05.2008)
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Lectures and tutorials in a lecture hall. Last update: T_KNM (17.05.2008)
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Written and oral part of the exam reflect the content of the course. Last update: STRAKOS/MFF.CUNI.CZ (29.04.2008)
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1. The Schur theorem, its consequences and connections. 2. Orthogonal transformations and QR decompositions. 3. The LU decomposition and its numerical stability. 4. The singular value decomposition, its theoretical and computational connections. 5. Least squares problems. 6. Partial eigenvalue problems. The Arnoldi method, the Lanczos method. 7. Iterative solution of linear algebraic systems. The conjugate gradient method and its generalizations. The generalized minimal residual method. 8. Computing of complete set of eigenvalues. The QR algoritm. Last update: STRAKOS/MFF.CUNI.CZ (29.04.2008)
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Students are expected to have attended the course NNUM105. Last update: T_KNM (22.05.2008)
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