ray.quot.seceig.general: Rayleigh quotient iteration

In EfficientMaxEigenpair: Efficient Initials for Computing the Maximal Eigenpair

Description

Rayleigh quotient iteration algorithm to computing the maximal eigenpair of matrix Q.

Usage

ray.quot.seceig.general(Q, mu, v0_tilde, zstart, digit.thresh = 6)

Arguments

Q	The input matrix to find the maximal eigenpair.
mu	A vector.
v0_tilde	The unnormalized initial vector \tilde{v0}.
zstart	The initial z_0 as an approximation of ρ(Q).
digit.thresh	The precise level of output results.

Value

A list of eigenpair object are returned, with components z, v and iter.

z	The approximating sequence of the maximal eigenvalue.
v	The approximating sequence of the corresponding eigenvector.
iter	The number of iterations.

Examples

Q = matrix(c(1, 1, 3, 2, 2, 2, 3, 1, 1), 3, 3)
ray.quot.seceig.general(Q, mu=rep(1,dim(Q)[1]), v0_tilde=rep(1,dim(Q)[1]), zstart=6,
 digit.thresh = 6)

Example output

$v
$v[[1]]
[1] 0.5773503 0.5773503 0.5773503

$v[[2]]
[1] -0.5144958 -0.6859943 -0.5144958

$v[[3]]
[1] 0.6491589 0.3964662 0.6491589

$v[[4]]
[1] -0.6479344 -0.4004521 -0.6479344

$v[[5]]
[1] -0.6479362 -0.4004466 -0.6479362


$z
$z[[1]]
[1] 6

$z[[2]]
[1] -5.176471

$z[[3]]
[1] -5.229846

$z[[4]]
[1] -5.236077

$z[[5]]
[1] -5.236068


$iter
[1] 4

EfficientMaxEigenpair documentation built on May 2, 2019, 2:17 a.m.