Results 1 to 2 of 2

Math Help - Quasi-Newton method with square root matrix

  1. #1
    Newbie
    Joined
    Jun 2009
    Posts
    7

    Quasi-Newton method with square root matrix

    Specifically, assume V is the covariance matrix, E its eigenvector matrix, and D the diagonal square root matrix of eigenvalues (on the diagonal), the update equation is

    x_{i+1} = x_i + EDZ'

    where Z is a matrix of independent rows(columns) of random standard normal variates. The other approach I have seen is to use

    x_{i+1} = x_i + Sqrt(V)Z'

    Is there a definition or theorem that would explain use of such square root matrices for quasi-Newton methods? What would the Z' matrix do to the step direction?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jun 2009
    Posts
    7

    Resolved

    Several reports stated that it's common to use the square root of the Hessian since its condition number (ratio of largest eigenvalue to smallest eigenvalue) is less severe.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Matrix that has square root
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 28th 2011, 12:54 PM
  2. Solve Using the Square Root Method
    Posted in the Algebra Forum
    Replies: 3
    Last Post: December 11th 2010, 08:42 PM
  3. Replies: 0
    Last Post: October 4th 2010, 01:24 AM
  4. The square root of a 2x2 matrix
    Posted in the Advanced Algebra Forum
    Replies: 6
    Last Post: July 10th 2010, 08:37 AM
  5. Square Root Method
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 25th 2009, 03:14 PM

Search Tags


/mathhelpforum @mathhelpforum