ray.quot.seceig.tri: Rayleigh quotient iteration for Tridiagonal matrix

In mxjki/EfficientMaxEigenpair: Efficient Initials for Computing the Maximal Eigenpair

Description

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

Usage

ray.quot.seceig.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

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[1] + c[1], a[1:N - 1] + b[2:N] + c[2:N], a[N] + c[N + 1]))
ray.quot.seceig.tri(Q, mu=rep(1,dim(Q)[1]), v0_tilde=rep(1,dim(Q)[1]), zstart=6,
 digit.thresh = 6)

mxjki/EfficientMaxEigenpair documentation built on May 24, 2019, 6:10 a.m.