# Computer science | NUMERICAL ANALYSIS

## Computer science NUMERICAL ANALYSIS

 0512100016 DIPARTIMENTO DI INFORMATICA COMPUTER SCIENCE 2013/2014

 OBBLIGATORIO YEAR OF COURSE 3 YEAR OF DIDACTIC SYSTEM 2008 PRIMO SEMESTRE
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/08 4 32 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS MAT/08 2 24 LAB SUPPLEMENTARY COMPULSORY SUBJECTS

 ANGELAMARIA CARDONE T
Objectives
1. KNOWLEDGE AND UNDERSTANDING
THE AIM OF THE COURSE, SCHEDULED IN TEACHER LESSONS AND LABORATORY ACTIVITIES, IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS CONCERNING THE BASIC TOPICS OF NUMERICAL ANALYSIS: FLOATING-POINT ARITHMETIC, NUMERICAL SOLUTION OF LINEAR SYSTEMS, COMPUTATION OF EIGENVALUES, APPROXIMATIONS OF DATA AND FUNCTIONS, CALCULUS OF DEFINITE INTEGRALS. PARTICULAR ATTENTION WILL BE PAID TO THE PRINCIPLES ABOUT THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE, WITH REGARD TO THE ESTIMATE OF ACCURACY OF THE OBTAINED RESULTS, THE EVALUATION OF THE PERFORMANCE OF THE DEVELOPED SOFTWARE, THE COMPARISON AMONG DIFFERENT METHODS, THE EXTERNAL AND INTERNAL DOCUMENTATION.
2. APPLYING KNOWLEDGE AND UNDERSTANDING
THE STUDENT SHOULD BE ABLE TO SOLVE PROBLEMS OF SCIENTIFIC CALCULUS, BY MEANS OF THE DEVELOPMENT AND THE USE OF MATHEMATICAL SOFTWARE AND SUITABLE COMPUTING ENVIRONMENT. HE SHOULD BE ABLE TO CHOOSE THE MOST SUITABLE NUMERICAL METHOD WITH RESPECT TO THE PROBLEM TO SOLVE, BY ANALYZING THE FEATURES OF THE PROBLEM, LIKE THE STRUCTURE OF THE DATA, THE REQUESTED ACCURACY AND THE STABILITY. FOR ANY TOPIC, IT WILL BE FURNISHED AN EXAMPLE WHICH REQUIRES THE APPLICATION OF THE CONSIDERED METHODS.
3. MAKING JUDGEMENTS
STUDENTS ARE GUIDED TO HARD LOOK TO WHAT THEY LEARN AND TO ENRICH THEIR MAKING JUDGMENTS SKILL BY STUDYING THE EDUCATIONAL MATERIAL. THE EVALUATION OF THE MATHEMATICAL SOFTWARE, BOTH DONE BY THEMSELVES OR JUST USED, AND THE COMPARISON AMONG DIFFERENT NUMERICAL METHODS, AIM TO DEVELOP THEIR MAKING JUDGMENTS SKILL AND THEIR CRITICAL SENSIBILITY.
4. COMMUNICATION SKILLS
THANKS TO THE LABORATORY ACTIVITIES, THE COURSE WILL HELP TO DEVELOP THE STUDENTS’ SKILL TO JUSTIFY AND TO CLAIM THE CHOICES MADE IN THE SOLUTION OF A COMPUTATIONAL PROBLEM, AND THE TEAMWORK SKILL.
5. LEARNING SKILLS
THE COURSE WILL GIVE THE BASIC MEANS TO LEARN NEW NUMERICAL METHODS AND TO USE OR DEVELOP NEW MATHEMATICAL SOFTWARE.
Prerequisites
ELEMENTS OF DISCRETE MATHEMATICS AND LINEAR ALGEBRA.
ELEMENTS OF MATHEMATICAL ANALYSIS: CONTINUOS FUNCTIONS AND MAIN THEOREMS, CONCEPTS OF DERIVATIVE AND INTEGRALS.
Contents
ERRORS ANALYSIS, PROPAGATION. ILL-CONDITIONING.
SYSTEMS OF LINEAR EQUAIONS. DIRECT METHODS: GAUSS AND LU FACTORIZATION. ITERATIVE METHODS: JACOBI, GAUSS-SEIDEL, RELAXATION. CONVERGENCE.
SISTEMI DI EQUAZIONI LINEARI. METODI DIRETTI: GAUSS E FATTORIZZAZIONE LU. METODI ITERATIVI: JACOBI, GAUSS – SEIDEL, RILASSAMENTO. CONVERGENZA.
EIGENVALUES OF MATRICES. ITERATIVE METHODS. QR METHOD.
APPROXIMATION. POLYNOMIAL INTERPOLATION: ERROR, STABILITY, CONVERGNECE. LINEAR PIECEWISE INTERPOLATION AND SPLINE.
LEAST SQUARES.