Can QR Method Accurately Approximate Eigenvalues? [SOLVED]

  • Context: Graduate 
  • Thread starter Thread starter angelz429
  • Start date Start date
  • Tags Tags
    Approximate Eigenvalues
Click For Summary
SUMMARY

The QR method effectively approximates the eigenvalues of the matrix [[4, 3], [3, 5]]. The actual eigenvalues are calculated as (9±√37)/2. This discussion emphasizes the importance of demonstrating prior work when seeking assistance, particularly in academic contexts. Participants are encouraged to engage with the material before requesting help to facilitate more productive discussions.

PREREQUISITES
  • Understanding of eigenvalues and eigenvectors
  • Familiarity with the QR algorithm for matrix factorization
  • Basic knowledge of linear algebra concepts
  • Ability to perform matrix operations and calculations
NEXT STEPS
  • Study the QR algorithm in detail for eigenvalue approximation
  • Learn about the convergence properties of the QR method
  • Explore numerical methods for solving eigenvalue problems
  • Review linear algebra textbooks focusing on eigenvalue computations
USEFUL FOR

Students, mathematicians, and data scientists interested in numerical linear algebra and eigenvalue approximation techniques.

angelz429
Messages
24
Reaction score
0
[SOLVED] Approximate eigenvalues

Use some QR method to approximate the eigenvalues of
[4 3]
[3 5]
and compare with the actual values.

The actual values are (9±√37)/2
 
Physics news on Phys.org
Didn't you read the files you were asked to when you registered?

You have now posted three consecutive questions (which look like homework and so should have been posted in the homework sections) without showing any work or any attermpt at a solution by yourself. You are required to show what you have done so we will know what kind of help you need.
 

Similar threads

Graduate Eigenvalues/eigenvectors using householder and QR
  • · Replies 5 ·
Replies
5
Views
5K
MHB Approximation of eigenvalue with inverse iteration method
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Eigenvalues of block matrix/Related non-linear eigenvalue problem
  • · Replies 1 ·
Replies
1
Views
2K
Graduate First eigenvalue not matching, but all others are
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Can one find a matrix that's 'unique' to a collection of eigenvectors?
  • · Replies 33 ·
2
Replies
33
Views
3K
MHB Solving Matrix A: Characteristic Equation and Eigenvectors
  • · Replies 2 ·
Replies
2
Views
2K
MHB Approximation of eigenvalue with power method
  • · Replies 21 ·
Replies
21
Views
4K
Graduate Solving algebraic equations that cannot be solved in radicals
  • · Replies 6 ·
Replies
6
Views
2K
Graduate The eigenvalue power method for quantum problems
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Types of complex matrices, why only 3?
  • · Replies 5 ·
Replies
5
Views
3K