Skip to main content
MathOverflow

Return to Question

Post Closed as "Not suitable for this site" by Gabriel C. Drummond-Cole, Carlo Beenakker, Tyrone, Pedro Lauridsen Ribeiro, Neil Strickland
added 171 characters in body
Source Link
Joshuashiing
Joshuashiing
  • 11
  • 2

I am working on an optimization problem (for example, conjugate gradient) to solve $Ax=b$, where $A$ is a symmetric positive definite matrix. I can understand that the CG (conjugate gradient) has better performance when the matrix $A$ has a smaller conditioner number. But I am wondering is there a relationship between the eigenvectors corresponding to the largest few eigenvalues and the first few update directions of the CG? Any suggestions would be helpful. Thanks!

(This question is also posted here.)

I am working on an optimization problem (for example, conjugate gradient) to solve $Ax=b$, where $A$ is a symmetric positive definite matrix. I can understand that the CG (conjugate gradient) has better performance when the matrix $A$ has a smaller conditioner number. But I am wondering is there a relationship between the eigenvectors corresponding to the largest few eigenvalues and the first few update directions of the CG? Any suggestions would be helpful. Thanks!

I am working on an optimization problem (for example, conjugate gradient) to solve $Ax=b$, where $A$ is a symmetric positive definite matrix. I can understand that the CG (conjugate gradient) has better performance when the matrix $A$ has a smaller conditioner number. But I am wondering is there a relationship between the eigenvectors corresponding to the largest few eigenvalues and the first few update directions of the CG? Any suggestions would be helpful. Thanks!

(This question is also posted here.)

Added top-level tag
Link
gmvh
gmvh
  • 3.1k
  • 6
  • 27
  • 46
Source Link
Joshuashiing
Joshuashiing
  • 11
  • 2

Conjugate gradient and the eigenvectors corresponding to the large eigenvalues

I am working on an optimization problem (for example, conjugate gradient) to solve $Ax=b$, where $A$ is a symmetric positive definite matrix. I can understand that the CG (conjugate gradient) has better performance when the matrix $A$ has a smaller conditioner number. But I am wondering is there a relationship between the eigenvectors corresponding to the largest few eigenvalues and the first few update directions of the CG? Any suggestions would be helpful. Thanks!