Efficient LSV Approximation for Large Matrices | Conjugate Gradient Method Guide

In summary, the person is looking for a quick approximation of the left singular vector and corresponding singular value for a large matrix G. They mention using the Conjugate Gradient method and are open to suggestions, such as Truncated SVD, for achieving this. They also clarify that they only need the left singular vector and largest singular value. They are looking for suggestions or examples on how to perform Truncated SVD.
  • #1
onako
86
0
For certain computations I need a quick approximation of the left singular vector of a matrix G( nxk ; n>k ). Also, the corresponding singular value would be needed. Perhaps after approximating the singular value I could use the Conjugate Gradient method to obtain the approximation of the left singular vector. Any idea on how to achieve this would be very welcome.
Note that for matrix G, n which is the number of rows, is very large ( n>>k).
Thanks
 
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  • #2
I read that Truncated SVD might be one of the solution for my problem:
http://en.wikipedia.org/wiki/Singular_value_decomposition#Truncated_SVD
Unfortunately, there are no examples I might use in order to implement this method.
Note that there is a need for Left singular vector (if it is not necessary to compute the Right singular vector) only
and the largest singular value (to be precise I need 2 LSVectors and the corresponding largest 2 singular values).
Any other suggestion on how to achieve this, or an example on how to perform Truncated SVD is very welcome.
 
  • #3
Anyone?
 

FAQ: Efficient LSV Approximation for Large Matrices | Conjugate Gradient Method Guide

What is Quick LSV approximation?

Quick LSV approximation is a method used in scientific research to quickly estimate the "local structure volume" (LSV) of a system. LSV is a measure of the amount of space available for a given molecule or atom in a given system.

How is Quick LSV approximation calculated?

Quick LSV approximation is calculated by dividing the total volume of the system by the number of atoms or molecules in the system. This gives an estimate of the average amount of space each atom or molecule occupies in the system.

What is the significance of Quick LSV approximation in scientific research?

Quick LSV approximation is significant because it allows for a quick estimation of the amount of space available for molecules or atoms in a given system. This information can be used to understand the properties and behavior of the system, as well as make predictions about how it may interact with other systems.

What are the limitations of Quick LSV approximation?

Quick LSV approximation is a simplified method and may not accurately reflect the true LSV of a system. It also does not take into account the shape and arrangement of molecules or atoms in the system, which can affect the available space. Additionally, it may not be applicable to complex systems with varying densities.

Are there any alternative methods to Quick LSV approximation?

Yes, there are other methods for calculating LSV, such as Monte Carlo simulations or molecular dynamics simulations. These methods may be more accurate but also require more computational resources and time to obtain results.

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