# 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

 1 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

 1 2 3 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.