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Numerical Analysis
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Precedente
Course data
Introduzione
Annunci
Monday 18/9/2023
Brief overview to introduce the course main concepts
Links for Lab
Homework : not compulsory, but suggested
Tuesday 19/9/2023
Representation of a Real Number
Floating-Point Numbers (or Finite Numbers)
Chopping versus Rounding
Thursday 21/9/2023
Finite Numbers that are Consecutive
Set of Finite Numbers (or toy computer)
Situations of Underflow or Overflow
Friday 22/9/2023
Representation in Computer Memory
IEEE Standard
Situations of Special Representation
Precision and Significant Digits
Machine Epsilon and Rounding (or Roundoff) Unit
Absolute Error and Relative Error
Monday 25/9/2023 LAB
Very simple and short introductory tutorial
Tuesday 26/9/2023
Finite (or Machine) Operations and IEEE rules
Finite Arithmetics
Thursday 28/9/2023
Nomenclature for Error Propagation
Types of Relative Error
Data Error and Inherent Error (Problem Conditioning)
Algorithmic Error (Method Stability)
Total Error (Output Accuracy)
Friday 29/9/2023
Error Analysis: one Finite Product of two Finite Numbers
EXAMPLE (numerical): one Finite product of two Real numbers
Error Analysis: one Finite product of two Real numbers
Error Analysis: one Finite sum of two Real numbers
Numerical Cancellation
Monday 2/10/2023
Measure of Conditioning
Examples of well conditioning and ill conditioning
Examples of ill conditioning resulting in numerical cancellation
Analyisis of the Conditioning of the problem "Find the roots of a polynomial"
Tuesday 3/10/2023
Measure of (Forward) Stability
Example of Unstability (i.e. no convergence) of an iterative method
The two components of the Algorithmic Error
Thursday 5/10/2023 - LAB
LAB : two functions that are equivalent analytically, but not numerically
LAB: more on Plot, Plot3D and Manipulate (visualizing input/output data is helpful)
Friday 6/10/2023
Polynomials
Other polynomial bases
Evaluation of a Polynomial
One polynomial, three different bases
Monday 9/10/2023
Conditioning of the Monomial Base
Bernestein Base
Newton Base
Thursday 12/10/2023
Interpolation
Minimal Degree
Interpolation in the Monomial Base (revised)
Friday 13/10/2023
Interpolation in the Bernstein Base
Interpolation in the Newton Base
Data Fitting
Monday 16/10/2023
Normal Equations
NormalEquations - Example in P1
Normal Equations - Example in P2
Polynomial Integration
Tuesday 17/10/2023
numerical linear algebra - intro
matrix condition number
Condition of a matrix
Thursday 19/10/2023
Permutation and Diagonal
Triangular matrix
LU Factorization
Successivo
Virtuale
Pannello laterale
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Numerical Analysis
Docente:
Giulia Spaletta
Anno Accademico
:
2023