Re: ? determine major singular pair


"Cheng Cosine" <acosine@xxxxxxxxxxxx> wrote in message
news:uRnkg.29137$JW5.1119@xxxxxxxxxxxxxxxxxxx
Hi:

The are methods to determine the major eigenpair of a square matrix A,

e.g., power method. But what if one is intereseted in determining the
major

singular pair of a rectangular matrix? That is those left and right
singular vectors

corresponding to the first largest singular values and those first largest
singular

values themself. Are there algorithm availabe?


Let's add some more conditions. A straightforward approach is to form

B = A^T*A and C = A*A^T and then one can use those methods for solving

a square matrix's major eigenpair to get singular pair. But this approach
has

a drawback on that when the larger dimension of square matrix A is big, say,

A is N-by-M and N is large, then A*A^T is N-by-N and requires significant

computer memory. Thus, a method does not require explicitly formulate

A*A^T is more desired.

Furthermore, in practice, one could face this situation that the explicit
form

of target rectangular matrix A is unknown. All one has are input vector and

corrresponding output vector: A*x = b, A is N-by-M, x is M-by-1, and b is
N-by-1.

Given one x, a vector b can be obtained, but A is unkwnon. This this case,
how does

one obtain A's singular pair? Or maybe we can star with a simpler case when
A

is a square matrix whose dimension is N-by-N, but entries remain unknown.

Thank,
by Cheng Cosine
Jun/16/2k6 NC


.

Relevant Pages

  • Linear algebra challenge answers
    ... Singular Value Decomposition (SVD), a function found on the HP48G and HP49G ... From an m x n matrix initially on the stack, ... The determinant of a square matrix is the product of its singular ...
    (comp.sys.hp48)
  • Linear algebra challenge answers
    ... Singular Value Decomposition (SVD), a function found on the HP48G and HP49G ... From an m x n matrix initially on the stack, ... The determinant of a square matrix is the product of its singular ...
    (comp.sys.hp48)
  • Re: ? determine major singular pair
    ... The are methods to determine the major eigenpair of a square matrix A, ... e.g., power method. ... That is those left and right singular ...
    (sci.math.num-analysis)
  • ? determine major singular pair
    ... The are methods to determine the major eigenpair of a square matrix A, ... e.g., power method. ... That is those left and right singular ...
    (sci.math.num-analysis)