shift.inv.tri {EfficientMaxEigenpair}

Shifted inverse iteration algorithm for Tridiagonal matrix

Description

Shifted inverse iteration algorithm algorithm to computing the maximal eigenpair of tridiagonal matrix Q.

Usage

shift.inv.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 \rho(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]))
shift.inv.tri(Q, mu=rep(1,dim(Q)[1]), v0_tilde=rep(1,dim(Q)[1]), zstart=6,
 digit.thresh = 6)