Lectures: 1) Well known errors in software and their aftermath, introduction to finite precision computation, rounding errors in basic linear algebra operations. 2) Rounding errors in basic linear algebra operations, upper error bounds. 3) Direct solvers in finite precision arithmetic, LU decomposition, Cholesky decomposition, pivoting. 4) Inverse of a triangular matrix in finite precision arithmetic, Kahan matrix. 5) Iterative solvers - stationary iterative methods (Jacobi, Gauss-Seidel, SOR, ...). 6) QR decomposition in finite precision arithmetic - schemes of the Gram-Schmidt orthogonalization process, Givens rotation, Householder reflection. 7) Rank-revealing algorithms, overdetermined/underdetermined system of linear algebraic equations. 8) Eigen decomposition, singular decomposition, Moore-Penrose pseudoinverse. 9) Nonlinear equations and their systems. 10) Numerical derivatives, difference formulas, order of accuracy. 11) Interpolation, approximation, regression, extrapolation. 12) Interpolation, approximation, regression, extrapolation. 13) Numerical integration, quadrature formulas. 14) Time reserve. Tutorials: 1) Linear algebra repeating (matrix notation, matrix multiplication, equation with matrices,...). 2) Rounding errors in basic linear algebra operations, upper error bounds. 3) Direct solvers, LU decomposition, Cholesky decomposition, pivoting. 4) Inverse of a triangular matrix in finite precision arithmetic, Kahan matrix. 5) Iterative solvers - stationary iterative methods (Jacobi, Gauss-Seidel, SOR, ?) 6) QR decomposition in finite precision arithmetic - schemes of the Gram-Schmidt orthogonalization process, Givens rotation, Householder reflection. 7) Rank-revealing algorithms, overdetermined/underdetermined system of linear algebraic equations. 8) Eigen decomposition, singular decomposition, Moore-Penrose pseudoinverse. 9) Nonlinear equations and their systems. 10) Numerical derivatives, difference formulas, order of accuracy. 11) Interpolation, approximation, regression, extrapolation. 12) Interpolation, approximation, regression, extrapolation. 13) Numerical integration. 14) Time reserve.
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Duintjer Tebbens E. J. ,Hnětynková I.,Plešinger M.,Strakoš Z.,Tichý P. Analýza metod pro maticové výpočty: Základní metody. Matfyzpress, 2012.
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Nicholas J. Higham. Accuracy and Stability of Numerical Algorithms. 2002.
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Segethová J. Základy numerické matematiky. Karolinum, 1998.
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