NUMERICAL ANALYSIS
Academic year and teacher
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- Versione italiana
- Academic year
- 2010/2011
- Teacher
- SILVIA BONETTINI
- Credits
- 6
- Curriculum
- INDUSTRIALE
- Didactic period
- Primo Trimestre
- SSD
- MAT/08
Training objectives
- The aim of the course is to make the students aware of the problems of the numerical processing, with respect to the floating point arithmetic and the computational complexity in the time and the space; numerical methods for the solution of some of the main problems of the scientific computing are introduced; their implementation and analysis are given by using interactive environments for the computing and the scientific visualization.
Prerequisites
- Basic notions of linear algebra and calculus.
Course programme
- Computer arithmetic: representation of the floating-point numbers and related operations; conditioning of a problem and stability of an algorithm; error propagation. Solution of systems of linear equations: direct methods (LU factorization, Choleski factorization, QR factorization) and iterative methods; perturbation and conditioning analysis. Nonlinear equations: convergence criteria and rate of convergence of iterative methods (bisection method, successive approximation method: secant and Newton methods). Approximation of data and functions: polynomial interpolation: Lagrange polynomial, Newton polynomial; interpolation by spline functions; linear least squares method. Implementation and analysis of the methods in the Matlab framework .
Didactic methods
- Theoretical/practical lessons.
Learning assessment procedures
- Written/oral examination.
Reference texts
- Burden R. L., Faires J.D., Numerical Analysis, Prindle Weber & Schmidt, Boston MA. 1985; Comincioli V., Analisi numerica: metodi modelli applicazioni. 2. ed. McGraw-Hill Italia, 1995.
