Skip to main content
MathOverflow

Return to Question

added 44 characters in body; edited tags; edited title
Source Link
Rodrigo de Azevedo
Rodrigo de Azevedo
  • 1
  • 3
  • 16
  • 35

Low rank Matrix-rank factorization of SPD matrix

Hello,

I'veI have a SPDsymmetric positive definite (SPD) matrix A; which$A$ that needs to be factorized as ${A=SS^{T}}$. ButHowever, using the Cholesky decomposition for this purpose is prohibitive in terms of computational cost. Moreover, the matrix is Densedense and has a slow decaying eigen-spectrum.

  Can anything be suggested for replacement of cholesky.Cholesky?

Moreover, it need not be exact,anything. Anything approximate will work as long as $y=Sz$ and the quantity $y^{T}y$ is what I'mI am trying to preserve.(, where $z$ is standard normal vector)

Thanks.

Low rank Matrix factorization

Hello,

I've a SPD matrix A; which needs to be factorized as ${A=SS^{T}}$. But, using Cholesky for this purpose is prohibitive in terms of computational cost. Moreover, matrix is Dense and has a slow decaying eigen-spectrum.

  Can anything be suggested for replacement of cholesky. Moreover, it need not be exact,anything approximate will work as long as $y=Sz$ and the quantity $y^{T}y$ is what I'm trying to preserve.($z$ is standard normal vector)

Thanks

Low-rank factorization of SPD matrix

I have a symmetric positive definite (SPD) matrix $A$ that needs to be factorized as ${A=SS^{T}}$. However, using the Cholesky decomposition for this purpose is prohibitive in terms of computational cost. Moreover, the matrix is dense and has a slow decaying eigen-spectrum. Can anything be suggested for replacement of Cholesky?

Moreover, it need not be exact. Anything approximate will work as long as $y=Sz$ and the quantity $y^{T}y$ is what I am trying to preserve, where $z$ is standard normal vector.

Source Link
arbitUser1401
arbitUser1401
  • 489
  • 4
  • 10

Low rank Matrix factorization

Hello,

I've a SPD matrix A; which needs to be factorized as ${A=SS^{T}}$. But, using Cholesky for this purpose is prohibitive in terms of computational cost. Moreover, matrix is Dense and has a slow decaying eigen-spectrum.

Can anything be suggested for replacement of cholesky. Moreover, it need not be exact,anything approximate will work as long as $y=Sz$ and the quantity $y^{T}y$ is what I'm trying to preserve.($z$ is standard normal vector)

Thanks