Eigen Initial Vector Weight ============================ .. code-block:: none Eigen Initial Vector Weight = 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.