Dajana CONTE | LABORATORY OF PROGRAMMING AND CALCULUS
Dajana CONTE LABORATORY OF PROGRAMMING AND CALCULUS
cod. 0512300006
LABORATORY OF PROGRAMMING AND CALCULUS
| 0512300006 | |
| DIPARTIMENTO DI MATEMATICA | |
| EQF6 | |
| MATHEMATICS | |
| 2017/2018 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2016 | |
| SECONDO SEMESTRE |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/08 | 6 | 48 | LESSONS |
| Objectives | |
|---|---|
| KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS THE THEORETICAL KNOWLEDGE AND CRITICAL ANALYSIS OF THE MAIN NUMERICAL METHODS CONCERNING THE BASIC TOPICS OF NUMERICAL ANALYSIS: NUMERICAL SOLUTION OF LINEAR SYSTEMS AND OF NONLINEAR EQUATIONS. PARTICULAR ATTENTION WILL BE PAID TO THE PRINCIPLES ABOUT THE DEVELOPMENT OF EFFICIENT MATHEMATICAL SOFTWARE IN C PROGRAMMING LANGUAGE, WITH REGARD TO THE ESTIMATE OF ACCURACY OF THE OBTAINED RESULTS AND THE EVALUATION OF THE PERFORMANCE OF THE DEVELOPED SOFTWARE. APPLYING KNOWLEDGE AND UNDERSTANDING: THE AIM OF THE COURSE IS TO MAKE THE STUDENT CAPABLE TO •SOLVE PROBLEMS LINEAR SYSTEMS AND NONLINEAR EQUATIONS BY USING MATHEMATICAL SOFTWARE AND SUITABLE CALCULUS ENVIRONMENTS •CHOOSE THE MORE APPROPRIATE NUMERICAL METHOD TO SOLVE THE PROBLEM UNDER EXAMINATION, BY MEANS OF THE ANALYSIS OF THE CHARACTERISTICS OF THE PROBLEM ITSELF. •STUDY THE CONVERGENCE OF AN ITERATIVE METHOD •RECOGNIZE ERRORS DERIVING FROM MACHINE OPERATIONS (IN FLOATING POINT ARITHMETIC) |
| Prerequisites | |
|---|---|
| BASIC LINEAR ALGEBRA (VECTOR AND MATRIX COMPUTATION, LINEAR SYSTEMS ...) AND MATHEMATICAL ANALYSIS (LIMITS, DERIVATIVES). CAN BE USEFUL SOME PRELIMINARIES OF PROGRAMMING (VARIABLES AND COSTANTS, LOOPS, LOGICAL CONDITIONS, C LANGUAGE). |
| Contents | |
|---|---|
| SOLVING A PROBLEM ON A COMPUTER: FROM THE REAL PROBLEM TO THE METHOD, TO THE ALGORITHM, TO THE PROGRAM, TO THE ANALYSIS OF RESULTS. ERROR SOURCES AND ERROR PROPAGATION. CONDITIONING OF A PROBLEM AND STABILITY OF AN ALGORITHM, SOURCES OF ERROR IN COMPUTATIONAL MODELS, MACHINES REPRESENTATION OF NUMBERS, THE FLOATING POINT NUMBER SYSTEM AND ARITHMETIC. EVALUATION OF AN ALGORITHM, SPACE AND TIME COMPLEXITY. EXAMPLES: COMPUTATION OF A DETERMINANT. VECTOR SPACES, NORMS. SYMMETRIC DEFINITE POSITIVE MATRICES, SYLVESTER CRITERION. CONDITIONING OF LINEAR SYSTEMS. DIRECT METHODS FOR SOLVING LINEAR SYSTEMS. SOLUTION OF TRIANGULAR SYSTEMS, BACK AND FORWARD SUBSTITUTION, COMPUTATIONAL COST. GAUSSIAN ELIMINATION METHOD. PIVOTING. LU FACTORIZAZION. CHOLESKY FACTORIZAZION. ITERATIVE METHODS FOR SOLVING LINEAR SYSTEMS: FORMULATIONS, CONVERGENCE, JACOBI, GAUSS SEIDEL AND SOR RELAXATION METHODS. ALGORITHMS BASED ON ITERATIVE METHODS: ERROR ESTIMATION AND STOP CRITERIA. SOLUTION OF NONLINEAR EQUATIONS. BISECTION METHOD. LOCAL LINEARIZATION METHODS. SECANT AND TANGENT (NEWTON) METHODS. CONVERGENCE. NEWTON'S METHOD FOR MULTIPLE ROOTS. FIXED POINT ITERATION. COMPUTATIONAL ASPECTS. CONDITIONING IN THE COMPUTATION OF THE ROOTS OF A POLYNOMIAL. DEVELOPMENT OF ALGORITHMS AND OF C PROGRAMS BASED ON THE MAIN STUDIED METHODS. |
| Teaching Methods | |
|---|---|
| LECTURES,PRACTICES,LABORATORY, PROJECTS |
| Verification of learning | |
|---|---|
| THE EXAM TEST EVALUATES THE ACQUIRED KNOWLEDGE AND THE ABILITY TO APPLY IT TO SOLVING TYPICAL PROBLEMS OF NUMERICAL ANALYSIS, ALSO THROUGH MATHEMATICAL SOFTWARE WRITTEN IN C LANGUAGE. IT IS DIVIDED INTO TWO TRIALS: A PRACTICAL TEST IN WHICH THE MATHEMATICAL SOFTWARE DESIGNED AND CONSTRUCTED DURING THE COURSE IS USED TO SOLVE SYSTEMS OF LINEAR EQUATIONS BY DIRECT AND ITERATIVE METHODS, AS WELL AS NONLINEAR EQUATIONS BY MEANS OF ITERATIVE LINEAR LOCALIZATION METHODS ; AN ORAL INTERVIEW, WITH THE PURPOSE OF ASSESSING THE THEORETICAL KNOWLEDGE PRESENTED IN THE LESSONS. DURING THE COURSE, A PRACTICAL TEST WILL BE CARRIED OUT WHICH EXEMPTS FROM THE PRACTICAL PART OF THE EVALUATION OF MATHEMATICAL SOFTWARE ON THE RESOLUTION OF SYSTEMS OF LINEAR EQUATIONS BY DIRECT AND ITERATIVE METHODS. |
| Texts | |
|---|---|
| G. MONEGATO – FONDAMENTI DI CALCOLO NUMERICO – ED. CLUT A. MURLI, G. GIUNTA, G. LACCETTI, M. RIZZARDI - LABORATORIO DI PROGRAMMAZIONE I, LIGUORI EDITORE A. MURLI - MATEMATICA NUMERICA: METODI, ALGORITMI E SOFTWARE, PARTE PRIMA, LIGUORI EDITORE V. COMINCIOLI - ANALISI NUMERICA: METODI, MODELLI, APPLICAZIONI - ED. MC GRAW HILL |
| More Information | |
|---|---|
| BEAPAT@UNISA.IT DAJCONTE@UNISA.IT |
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