How do i construct a design matrix for a least square problem?

  • Context: Graduate 
  • Thread starter Thread starter papasmurfff
  • Start date Start date
  • Tags Tags
    Design Matrix Square
Click For Summary
SUMMARY

To construct a design matrix for a least squares problem when fitting a polynomial of degree n-1 to a function f(t) using values at points z = [z1; z2; ...; zm], the matrix A is formed by evaluating the polynomial basis functions at the points z. The vector b is constructed from the function values f(z). The relationship between t and z must be clearly defined to ensure accurate construction of the least squares problem Ax = b.

PREREQUISITES
  • Understanding of polynomial regression and least squares fitting
  • Familiarity with matrix notation and operations
  • Knowledge of function evaluation at discrete points
  • Basic concepts of linear algebra
NEXT STEPS
  • Study polynomial basis functions for least squares fitting
  • Learn about constructing design matrices in NumPy
  • Explore the relationship between independent and dependent variables in regression
  • Investigate the use of libraries like SciPy for optimization problems
USEFUL FOR

Data scientists, statisticians, and anyone involved in regression analysis or polynomial fitting will benefit from this discussion.

papasmurfff
Messages
3
Reaction score
0
Suppose we want to to fit an arbitrary function f(t) with a polynomial of
degree n - 1 using the values of the function in an arbitrary set of points z = [z1; z2; : : : ; zm].

how would do i construct the least squares problem Ax=b. in other words, how would i construct the matrix A and b in terms of f(t) and z ?
 
Physics news on Phys.org
...using the values of the function in an arbitrary set of points z...

Not sure what you mean here. Do you know the relationship of t to z?
 

Similar threads

Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K
Building a least square problem design matrix
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Linear least-squares method and row multiplication of matrix
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How Does Least Squares Determine the Mean and Variance?
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad General form of symmetric 3x3 matrix with only 2 eigenvalues
  • · Replies 4 ·
Replies
4
Views
6K
Graduate Structure of modulo-integer matrix group GL(r,Z(n))?
  • · Replies 17 ·
Replies
17
Views
7K
Undergrad What is Nonlinear Least Squares in Regression Analysis?
  • · Replies 4 ·
Replies
4
Views
2K
MHB Square Matrix Proof: Diagonal Entries & Properties
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Convergence issue in this Least Squares calculation
  • · Replies 2 ·
Replies
2
Views
2K
Graduate How do I find the change of basis matrix for the JCF of M?
  • · Replies 6 ·
Replies
6
Views
2K