Numerical analysis
1999/2000. Mathematics.
Contents:
Basic notions about numerical analysis. Error theory, numerical
solution of linear systems, the eigenvalue problem, nonlinear equations,
approximation of functions, quadrature formulae for numerical integration,
numerical solution of the Cauchy problem.
Program:
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Error theory and floating-point representation.
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Numerical solution of linear systems: direct and iterative methods.
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Numerical computation of eigenvalues.
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Numerical solution of nonlinear equations: bisection, regula falsi,
secant method, Newton method.
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Approximation of functions: interpolation, least squares, cubic splines,
best approximation.
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Quadrature formulae: simple and composite Newton-Cotes, Gaussian formulae.
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Cauchy problem: one-step methods (Runge-Kutta),
multistep methods.
References:
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V. Comincioli, Analisi Numerica, Metodi Modelli Applicazioni. McGraw Hill
Libri Italia, Milano, 1990.
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A. Quarteroni, R. Sacco, F. Saleri,
Matematica numerica.
Springer-Verlag Italia, Milano, 1998.
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K. Atkinson,
An introduction to numerical analysis.
Ricevimento:
Dopo le lezioni in studio.