functionLeastSquares
Information
Hypothesis and equations
Given a cloud of N points (xi, yi), the best degree polynomial q 
which minimizes 
.
Finding the polynomial P means finding the vector 
which minimizes the norm 
avec 
and y the vector {yi}i=1,N.
Bibliography
none
Instructions for use
Example with Excel : we seek a polynomial trend curve of degree 3 with the following cloud of points :
Known limits / Use precautions
none
Validations
Validated function - Hassan Bouia, Sila Filfli 02/2011
--------------------------------------------------------------
Licensed by EDF under a 3-clause BSD-license
Copyright © EDF 2009 - 2023
BuildSysPro version 3.6.0
Author : Hassan BOUIA, Sila FILFLI, EDF (2011)
--------------------------------------------------------------
Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| Integer | N | 6 | Number of points |
| Integer | q | 3 | Degree of the sought polynomial |
| Real[N] | x | {1., 2, 3, 4, 5, 7} | X-axis |
| Real[N] | y | {1, 2, 3.2, 4, 4.5, 7.2} | Y-axis |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real[q + 1] | c | Coefficients of the sought polynomial |
Revisions
Benoît Charrier 01/2016 : Adaptation pour compatibilité avec OpenModelica