Numerical Analysis 1
A.Y. 2018/2019
Learning objectives
The aim of the course is to provide students with the basic methods of the Numerical Analysis with examples from the scientific computing.
Expected learning outcomes
Learning of the basic methods and algorithms for solving some mathematical problems including: data and function approximation, linear system resolution, computation of the zeros of nonlinear functions, quadrature formula, approximation of eigenvalues. Students will also be able to implement the learned algorithms using the MATLAB software.
Lesson period: First semester
Assessment methods: Esame
Assessment result: voto verbalizzato in trentesimi
Single course
This course cannot be attended as a single course. Please check our list of single courses to find the ones available for enrolment.
Course syllabus and organization
Single session
Responsible
Lesson period
First semester
Course syllabus
Why numerical analysis. Floating-Point Representation and errors,
stability of computations. Condition Number and ll-Conditioning, stability of algorithms and problems. Examples from scientific computing. Interpolation and approximations of functions and data. e di dati. Polynomial Interpolation: Lagrange form, Newton form. Algorithm for interpolation. Errors in Polynomial Interpolation. Chebyshev polynomial Interpolation. Introduction of Spline functions, linear and cubic case. Smoothing of Data and
the Method of Least Squares. Numerical Integration and interpolation. Newton-Cotes quadrature formula. Error Analysis.
Composite rules. Gaussian Quadrature Formulas.
Locating Roots of Equations: bisection, secant, Newton. Fixed point
iteration. Convergence analysis, end test. Numerical solution of systems of linear equations, error analysis and condition. A) Direct method. Tridiagonal and Banded Systems. Gaussian Elimination, LU factorization, Pivoting. Other factorization0. B) Iterative methods. Convergence, analysis and errors. Splitting, Jacobi and Gauss-Seidel method, SOR, Richardson.
Calculating Eigenvalues and Eigenvectors, Localization (Gershgorin's Theorem). Power method.
stability of computations. Condition Number and ll-Conditioning, stability of algorithms and problems. Examples from scientific computing. Interpolation and approximations of functions and data. e di dati. Polynomial Interpolation: Lagrange form, Newton form. Algorithm for interpolation. Errors in Polynomial Interpolation. Chebyshev polynomial Interpolation. Introduction of Spline functions, linear and cubic case. Smoothing of Data and
the Method of Least Squares. Numerical Integration and interpolation. Newton-Cotes quadrature formula. Error Analysis.
Composite rules. Gaussian Quadrature Formulas.
Locating Roots of Equations: bisection, secant, Newton. Fixed point
iteration. Convergence analysis, end test. Numerical solution of systems of linear equations, error analysis and condition. A) Direct method. Tridiagonal and Banded Systems. Gaussian Elimination, LU factorization, Pivoting. Other factorization0. B) Iterative methods. Convergence, analysis and errors. Splitting, Jacobi and Gauss-Seidel method, SOR, Richardson.
Calculating Eigenvalues and Eigenvectors, Localization (Gershgorin's Theorem). Power method.
MAT/08 - NUMERICAL ANALYSIS - University credits: 9
Practicals: 33 hours
Laboratories: 24 hours
Lessons: 36 hours
Laboratories: 24 hours
Lessons: 36 hours
Shifts:
Professors:
Naldi Giovanni, Zampieri Elena
Turno A
Professor:
Causin PaolaTurno B
Professor:
Zampieri ElenaTurno C
Professor:
Zampieri ElenaProfessor(s)