QR Decomposition w/ Householder and Givens Transformations

Click For Summary
SUMMARY

This discussion focuses on QR decomposition using Householder and Givens transformations, specifically in the context of solving regression problems. QR decomposition is utilized to minimize residuals instead of forming normal equations, making it essential for linear least squares problems. A valuable resource provided is a lecture note from the University of Texas at Arlington, which includes examples and explanations relevant to the topic. The actual problem begins on page 11, with introductory material on pages 1-10.

PREREQUISITES
  • Understanding of linear algebra concepts, particularly matrix decomposition
  • Familiarity with QR decomposition techniques
  • Knowledge of regression analysis and least squares methods
  • Basic proficiency in mathematical problem-solving
NEXT STEPS
  • Study the provided lecture notes on QR decomposition from the University of Texas at Arlington
  • Explore detailed examples of linear least squares problems using QR decomposition
  • Learn about Householder transformations and their application in QR decomposition
  • Investigate Givens transformations and how they differ from Householder transformations
USEFUL FOR

Students and professionals in mathematics, data science, and engineering who are interested in advanced regression techniques and matrix decomposition methods.

Th3HoopMan
Messages
7
Reaction score
0
Could anybody link me to some good examples on how to go about doing them? I honestly have no idea how to go about doing these two types of problems.
 
Physics news on Phys.org
Th3HoopMan said:
Could anybody link me to some good examples on how to go about doing them? I honestly have no idea how to go about doing these two types of problems.
It's not clear what you are looking for here.

Do you want to know how to develop QR decomposition using HH & Givens Transforms?
Or
Are you looking for examples of problems which can be solved using QR decomposition?
 
SteamKing said:
It's not clear what you are looking for here.

Do you want to know how to develop QR decomposition using HH & Givens Transforms?
Or
Are you looking for examples of problems which can be solved using QR decomposition?
Examples of problems which can be solving using QR
 
Th3HoopMan said:
Examples of problems which can be solving using QR
Just about any regression problem where the number of data points exceeds the degree of the curve being fitted.

You use QR to find the minimum of the residuals in place of forming the normal equations.

Here is an example using linear least squares:

http://www.uta.edu/faculty/rcli/Teaching/math5392/NotesByHyvonen/lecture3.pdf

Note: actual problem starts on p. 11, but there is a good intro. in pp. 1-10. :smile:
 
SteamKing said:
Just about any regression problem where the number of data points exceeds the degree of the curve being fitted.

You use QR to find the minimum of the residuals in place of forming the normal equations.

Here is an example using linear least squares:

http://www.uta.edu/faculty/rcli/Teaching/math5392/NotesByHyvonen/lecture3.pdf

Note: actual problem starts on p. 11, but there is a good intro. in pp. 1-10. :smile:
Thank you!
 

Similar threads

MHB QR Decomposition and Full Column Rank of A
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Want to understand how to express the derivative as a matrix
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Proof by induction of block diagonal decomposition of a matrix
  • · Replies 4 ·
Replies
4
Views
2K
High School What unique contributions to math did linear algebra make?
  • · Replies 19 ·
Replies
19
Views
4K
Undergrad Passive Transformation and Rotation Matrix
  • · Replies 1 ·
Replies
1
Views
4K
Undergrad Can't understand a step in an LU decomposition proof
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Given two linear transformations L and K, show ##K = \lambda L## holds
  • · Replies 9 ·
Replies
9
Views
2K
Undergrad Row space, Column space, Null space & Left null space
  • · Replies 8 ·
Replies
8
Views
3K
Undergrad Confused about small detail in rank-nullity theorem
  • · Replies 1 ·
Replies
1
Views
2K