QR Decomposition w/ Householder and Givens Transformations

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Discussion Overview

The discussion revolves around QR decomposition using Householder and Givens transformations, focusing on understanding the methods and their applications, particularly in solving regression problems.

Discussion Character

  • Homework-related
  • Technical explanation

Main Points Raised

  • Some participants express uncertainty about how to approach QR decomposition using Householder and Givens transformations.
  • There is a request for clarification on whether the interest lies in developing the QR decomposition methods or in examples of problems that can be solved using QR decomposition.
  • One participant suggests that QR decomposition can be applied to regression problems where the number of data points exceeds the degree of the curve being fitted.
  • A specific example related to linear least squares is provided, with a link to additional resources for further reading.

Areas of Agreement / Disagreement

Participants generally agree on the applicability of QR decomposition to regression problems, but there is no consensus on the specific examples or methods being sought.

Contextual Notes

The discussion lacks clarity on the specific examples or methods participants are interested in, and there are repeated requests for clarification on the original inquiry.

Th3HoopMan
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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.
 
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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!
 

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