# ray.quot.tri: Rayleigh quotient iteration for Tridiagonal matrix In EfficientMaxEigenpair: Efficient Initials for Computing the Maximal Eigenpair

## Description

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

## Usage

 1 ray.quot.tri(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 eigenfunction of the corresponding eigenvector. iter The number of iterations.

## Examples

 1 2 3 4 5 6 7 8 a = c(1:7)^2 b = c(1:7)^2 c = rep(0, length(a) + 1) c[length(a) + 1] = 8^2 N = length(a) Q = tridiag(b, a, -c(b + c, a[1:N - 1] + b[2:N] + c[2:N], a[N] + c[N + 1])) ray.quot.tri(Q, mu=rep(1,dim(Q)), v0_tilde=rep(1,dim(Q)), zstart=6, digit.thresh = 6) 

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