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Ingénierie Informatique (Academic Year 2018/2019) - Programmazione e sicurezza
Numerical methods
Slides
Leçon n. 1:
Introduction to the Course
Introduction to the Course
Course Objectives
Course Outline
MATLAB presentation
Leçon n. 2:
Computer Arithmetic
Contents
Computer arithmetic
Numerical cancellation
Questions
Leçon n. 3:
Introduction to MATLAB
Contents
Basic features and commands
Questions
Leçon n. 4:
The MATLAB programming language
Contents
More MATLAB commands
M-files
Questions
Leçon n. 5:
Numerical problems and algorithms
Contents
Conditioning of a numerical problem
Stability of an algorithm
Leçon n. 6:
Linear Systems
Contents
Vectors and matrices
Linear systems - Preliminaries
Questions
Leçon n. 7:
Gauss elimination method
Contents
The classical Gauss elimination method
Partial pivoting
Gauss method with partial pivoting
Questions
Leçon n. 8:
Gauss algorithm
Contents
Gauss algorithm
Questions
Leçon n. 9:
Matrix decompositions
Contents
Matrix decompositions
Questions
Leçon n. 10:
Iterative methods for linear systems
Contents
Classical iterative methods
Jacobi method
Gauss - Seidel method
SOR method
Questions
Leçon n. 11:
More on MATLAB programming
Contents
More on MATLAB programming
Computation of the eigenvalues of a matrix (basic ideas)
Questions
Leçon n. 12:
Polinomial interpolation (I)
Inizio
Contents
Polinomial interpolation
Lagrange’s formula
Newton’s formula
Leçon n. 13:
Polinomial interpolation (II)
Contents
Newton’s formula
Choice of the interpolation nodes
Convergence
Leçon n. 14:
Piecewise polynomial interpolation
Contents
MATLAB commands and questions on polynomial interpolation
Questions
Interpolation with piecewise polynomial functions
Leçon n. 15:
Cubic splines
Contents
Interpolation with piecewise polynomial functions
Cubic splines
Leçon n. 16:
Final comments on interpolation
Contents
Questions on cubic splines
Interpolation of a function in a bounded interval
MATLAB experiments
Leçon n. 17:
Least squares fitting
Contents
Least squares
MATLAB commands
Questions
Leçon n. 18:
Non linear equations
Contents
Preliminaries
The secant method
The tangent (or Newton’s) method
The fixed-point method
Leçon n. 19:
Numerical integration (I)
Contents
Quadrature formulas of interpolatory type
Newton-Cotes formulas
Leçon n. 20:
Numerical integration (II)
Contents
Orthogonal polynomials
Gaussian formulas
Composite formulas
MATLAB commands
Questions
Leçon n. 21:
Some computation using MATLAB
Contents
Roots of equations
Computation of integrals
Leçon n. 22:
Initial value problems for ODEs
Contents
Ordinary Differential Equations
Initial value problems (Cauchy problems)
Canonical form of a Cauchy problem
Leçon n. 23:
Numerical methods for initial value problems (I)
Contents
Numerical methods
One-step methods
Multistep methods
Examples
Leçon n. 24:
Numerical methods for initial value problems (II)
Contents
Numerical methods
MATLAB commands
Leçon n. 25:
Scientific computation using MATLAB
Contents
Questions
MATLAB computation
Overall conclusions