NUMERICAL ANALYSIS AND LABORATORY
Academic year and teacher
If you can't find the course description that you're looking for in the above list,
please see the following instructions >>
- Versione italiana
- Academic year
- 2016/2017
- Teacher
- VALERIA RUGGIERO
- Credits
- 9
- Didactic period
- Primo Semestre
- SSD
- MAT/08
Training objectives
- The course's objective is the teaching of the basic tools in order to be able to face the main problems of scientific computing and to analyse stability and effectiveness of the related software.
Main knowledge learned are:
- topics concerning numerical computation, related to finite arithmetic and computational complexity in terms of space and time;
- numerical methods for solving some of the main problems of scientific computing (solution of linear systems, data approximation, numerical integration, solution of nonlinear equations) and related analysis in terms of complexity and stability.
The key capabilities gained are:
- ability to solve the main problems of scientific computing environments through the use of interactive computing and scientific visualization and ability to analyse the results obtained;
- ability to use the tools of discrete mathematic for developing software. Prerequisites
- The following concepts and the knowledge provides by the courses of “Matematica Discreta (Discrete Mathematics)” and “Istituzioni di Matematica (Elements of Mathematics)” are mandatory:
-Linear Algebra (vector spaces, linear applications, matrix computing, Euclidean spaces, eigenvalues and eigenvectors, quadratic forms)
-real numbers, functions, sequences, function's limits, derivatives, integrals, basis of complex numbers.
It is also highly recommended to have skills and abilities on basic tools of programming. Course programme
- MatLab: usage and principal functions
Computer arithmetic: finite number representation and related operations, condition of a problem and stability of an algorithm; error propagation
Linear systems: triangular systems, direct methods (LU factorization, Choleski factorization, QR factorization); sparse matrix methods
Linear systems: perturbation analysis and condition number
Linear systems: iterative methods
Polynomial interpolation: Lagrange polynomial, Newton polynomial, Hermite polynomial; interpolation error; Chebyshev knots; interpolation by spline functions
Approximation of data and functions via least squares method
Newton-Cotes formulae for interpolated integration; composite formulea
Methods for solving nonlinear equations. Didactic methods
- 72 hours are scheduled, divided in lectures and exercises. In particular, 54 hours are dedicated to the lectures and 18 hours dedicated to guided tutorial in computing lab.
The course is organized as follows:
- lectures on all the couse's topics
- exercises in I.T. laboratory dedicated to the acquisition of the principal skills regarding the MatLab environment and the realization of the main methods studied in class.
In order to support the practical lessons, a laboratory activity with a laboratory assistant is scheduled for further exercises, to strengthen the concepts acquired in class. Learning assessment procedures
- The objective of the final exam consists in verifying the level of knowledge of the formative objectives previously stated.
The final exam consists in a written test, with both theoretical and practical questions.
The theoretical ones aim to verify the acquisition and the comprehension of the main topics of the course.
The practical questions regard problems whose solution must be obtained by writing MatLab code, and the results must be properly commented.
The available time for the final test is 4 hours.
The students will have access to a PC equipped by Matlab for the practical part; the code and related results and comments must be written down.
Students will not be allowed to consult texts.
The evaluation of the answers to the theoretical questions is based on the correctness, on the clarity and on the completeness of the script.
The evaluation of answers to the practical questions is based on the syntactic and semantic correctness of the code, on the efficacy and effictiveness of the methods for finding the required solution and on the ability in analysing the results.
A score is assigned to each question. The text is considered successfully passed if a score of almost 9 is reached in the theoretical part and a score of almost 9 is reached in the practical part. The final mark ranges between 18 and 30, depending on the number of the answered questions and on the quality of the answers. Reference texts
- Teacher’s handouts
Burden R. L., Faires J.D., Numerical Analysis, Prindle Weber & Schmidt, Boston MA. 2004;
Insights: Quarteroni A., Saleri F., Sacco R.: Matematica numerica, Springer Verlag, 2008;
Galligani I.: Elementi di Analisi Numerica, Calderini editrice Bologna, 1986.
