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B012513 - ADVANCED TOPICS OF NUMERICAL ANALYSIS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Prerequisites
Teaching Methods
Further information
Type of Assessment
Course program
Academic Year 2011-12
Coorte 2011 - Second Cycle Degree in COMPUTER SCIENCE
Course year
First year -
Belonging Department
Statistics, IT and its applications "G. Parenti" (DISIA)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
6
Teaching Hours
48
Teaching Term
⇒
Attendance required
No
Type of Evaluation
Final Grade
Course Content
show
Course program
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Lectureship
Mutuality
Course teached as:
B005508 - ANALISI NUMERICA II
3-years First Cycle Degree (DM 270/04) in MATEMATICA
Curriculum APPLICATIVO
B005508 - ANALISI NUMERICA II
3-years First Cycle Degree (DM 270/04) in MATEMATICA
Curriculum APPLICATIVO
Teaching Language
Italian
Course Content
Polynomial and trigonometric least squares data-fitting. Discrete Fourier transform. Numerical solution of linear least squares problems. Introduction to the singular value decomposition (SVD). Conjugate gradient method for positive definite linear systems. Using QR factorization, SVD and CG to solve linear least squares problems. Runge-Kutta methods for initial value problems.
Suggested readings (Search our library's catalogue)
Bini, Capovani, Menchi, "Metodi Numerici per l’Algebra Lineare", Ed. Zanichelli, Bologna, 1993.
Fausett, “Applied Numerical Analysis Using Matlab”, Prentice Hall, NJ, 1999.
Gautschi, “Numerical Analysis. An Introduction”, Birkhäuser, Boston, 1997
Fausett, “Applied Numerical Analysis Using Matlab”, Prentice Hall, NJ, 1999.
Gautschi, “Numerical Analysis. An Introduction”, Birkhäuser, Boston, 1997
Learning Objectives
Knowledge acquired:
The course deals with the definition and study of methods for solving mathematical problems by using computers.
Purpose of the course is to complete the presentation of the basic methodologies of numerical analysis, by discussing the numerical solution of ordinary differential equations, of eigenvalue problems, and of problems arising in polynomial and trigonometric approximation, with a particular attention devoted to implementation issues.
Competence acquired:
Knowledge of classical numerical methods for computing eigenvalues and eigenvectors of matrices, of the techniques for polynomial and trigonometric approximations, and of one step methods for solving initial value problems in ordinary differential equations.
Skills acquired (at the end of the course):
Ability to develop simple programs and to use software available in Matlab in order to solve the mathematical problems under study. Understanding of the obtained numerical results.
The course deals with the definition and study of methods for solving mathematical problems by using computers.
Purpose of the course is to complete the presentation of the basic methodologies of numerical analysis, by discussing the numerical solution of ordinary differential equations, of eigenvalue problems, and of problems arising in polynomial and trigonometric approximation, with a particular attention devoted to implementation issues.
Competence acquired:
Knowledge of classical numerical methods for computing eigenvalues and eigenvectors of matrices, of the techniques for polynomial and trigonometric approximations, and of one step methods for solving initial value problems in ordinary differential equations.
Skills acquired (at the end of the course):
Ability to develop simple programs and to use software available in Matlab in order to solve the mathematical problems under study. Understanding of the obtained numerical results.
Prerequisites
Courses recommended: first level courses of numerical analysis and Matlab.
Teaching Methods
Total hours of the course (including the time spent in attending lectures, seminars, private study, examinations, etc...): 150
Hours reserved to private study and other indivual formative activities: 102
Contact hours for: Lectures (hours): 30
Contact hours for: Laboratory (hours):18
Hours reserved to private study and other indivual formative activities: 102
Contact hours for: Lectures (hours): 30
Contact hours for: Laboratory (hours):18
Further information
equency of lectures, practice and lab: Recommended
Teaching Tools
UniFi E-Learning: http://e-l.unifi.it
Office Hours:
Wednesdays, 14.00-16.00 or by appointment.
Dipartimento di Energetica "Sergio Stecco".
Viale Morgagni, 40/44 - 50134 Firenze
Tel. 055 4796716
Fax. 055 4796744
alessandra.papini@unifi.it
Teaching Tools
UniFi E-Learning: http://e-l.unifi.it
Office Hours:
Wednesdays, 14.00-16.00 or by appointment.
Dipartimento di Energetica "Sergio Stecco".
Viale Morgagni, 40/44 - 50134 Firenze
Tel. 055 4796716
Fax. 055 4796744
alessandra.papini@unifi.it
Type of Assessment
Oral
Course program
Polynomial and trigonometric least squares data-fitting; trigonometric interpolation. Discrete Fourier transform. Linear least squares problems: basic concepts and characterization of the solutions via normal equations. Introduction to the singular value decomposition (SVD). Conjugate gradient method for positive definite linear systems. Using QR factorization, SVD and CG to solve linear least squares problems. Runge-Kutta methods for initial value problems; basic concepts on convergence, consistency and stability.