Eigen Initial Vector Weight

Eigen Initial Vector Weight = <float>

Description/Usage

This optional card allows the user to modify the initial vector used within the eggroll eigensolver to contruct a Krylov subspace. Legal inputs are:

w

A scale factor for the amount of uniform randomness to apply to each component of the initial vector.

The default value of w is 0.5.

Examples

Here is a sample card:

Eigen Initial Vector Weight = 0.1

Technical Discussion

Because of the way a Krylov space is generated, it is very important that the initial vector contain some component in the direction of the eigenvector. By adding a random vector to the initial vector this can be guaranteed. A random vector r is constructed to have components from U[0,1] (uniform distribution). It is then normalized to have length 1. The initial vector is then modifed as x = w * r + (1-w) * x. The effect this value has should be minimal for w not equal to 0 or 1.

This card is not applicable to the ARPACK eigensolver.

Theory

No Theory.

FAQs

No FAQs.

References

No References.