eff.ini.maxeig.shift.inv.tri {EfficientMaxEigenpair}

Tridiagonal matrix maximal eigenpair

Description

Calculate the maximal eigenpair for the tridiagonal matrix by shifted inverse iteration algorithm.

Usage

eff.ini.maxeig.shift.inv.tri(a, b, c, xi = 1, digit.thresh = 6)

Arguments

a

The lower diagonal vector.

b

The upper diagonal vector.

c

The shifted main diagonal vector. The corresponding unshift diagonal vector is -c(b[1] + c[1], a[1:N - 1] + b[2:N] + c[2:N], a[N] + c[N + 1]) where N+1 is the dimension of matrix.

xi

The coefficient used to form the convex combination of \delta_1^{-1} and (v_0,-Q*v_0)_\mu, it should between 0 and 1.

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.

See Also

eff.ini.maxeig.tri for the tridiagonal matrix maximal eigenpair by rayleigh quotient iteration algorithm. eff.ini.maxeig.general for the general matrix maximal eigenpair.

Examples

a = c(1:7)^2
b = c(1:7)^2
c = rep(0, length(a) + 1)
c[length(a) + 1] = 8^2
eff.ini.maxeig.shift.inv.tri(a, b, c, xi = 1)