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B018805 - TOPICS IN NUMERICAL ANALYSIS
Main information
Teaching Language
Course Content
Suggested readings
Learning Objectives
Teaching Methods
Type of Assessment
Academic Year 2013-14
Coorte 2013 - Second Cycle Degree in MATHEMATICS
Course year
First year - Second Semester
Belonging Department
Mathematics and Computer Science "Ulisse Dini" (DIMAI)
Course Type
Single education field course
Scientific Area
MAT/08 - NUMERICAL ANALYSIS
Credits
9
Teaching Hours
72
Teaching Term
03/03/2014 ⇒ 13/06/2014
Attendance required
No
Type of Evaluation
Final Grade
Course Content
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Lectureship
Teaching Language
Italian
Course Content
Splines: the B-spline basis, theorem of Curry-Schoenberg, spline interpolation and least-squares approximation, applications to graphics, tensor-product splines.
Advanced numerical schemes for conservative problems: introduction of HBVM methods based on Fourier approximation, their formulation as Runge-Kutta methods. Line Integral Methods.
Iterative methods for linear and non-linear system: Krylov methods; inexact Newton methods; preconditioning.
Advanced numerical schemes for conservative problems: introduction of HBVM methods based on Fourier approximation, their formulation as Runge-Kutta methods. Line Integral Methods.
Iterative methods for linear and non-linear system: Krylov methods; inexact Newton methods; preconditioning.
Suggested readings (Search our library's catalogue)
De Boor, C. “ A Practical Guide to Splines” II ed., Springer, Berlin, 2001.
Kelley, “Iterative Methods for Linear and Nonlinear Equations”, Frontiers in Applied Mathematics, v. 16, SIAM, Philadelphia, 1995.
Lecture notes on Line Integral Methods, disponibile al link: http://arxiv.org/abs/ 1301.2367
Kelley, “Iterative Methods for Linear and Nonlinear Equations”, Frontiers in Applied Mathematics, v. 16, SIAM, Philadelphia, 1995.
Lecture notes on Line Integral Methods, disponibile al link: http://arxiv.org/abs/ 1301.2367
Learning Objectives
Knowledge acquired: deepened knowledge on advanced methodologies and related algorithmic aspects of current interest in the Numerical Analysis field, also outlining their use for applications. The course also shows how the considered methods perform, via their implementation and experimentation in Matlab.
Competence acquired: advanced competence in numerical linear algebra and approximation, as well as in numerical modelling of conservative differential problems.
Skills acquired: being able to select, use and compare numerical methods suited to solve the considered problems. Being also able to evaluate the numerical results.
Competence acquired: advanced competence in numerical linear algebra and approximation, as well as in numerical modelling of conservative differential problems.
Skills acquired: being able to select, use and compare numerical methods suited to solve the considered problems. Being also able to evaluate the numerical results.
Teaching Methods
Traditional lessons and exercise sections in a computer lab
Type of Assessment
Oral exam