# eff.ini.seceig.tri: Tridiagonal matrix next to the maximal eigenpair In EfficientMaxEigenpair: Efficient Initials for Computing the Maximal Eigenpair

## Description

Calculate the next to maximal eigenpair for the tridiagonal matrix whose sums of each row should be 0.

## Usage

 `1` ```eff.ini.seceig.tri(a, b, xi = 1, digit.thresh = 6) ```

## Arguments

 `a` The lower diagonal vector. `b` The upper diagonal vector. `xi` The coefficient used in the improved initials to form the convex combination of δ_1^{-1} and (v_0,-Q*v_0)_μ, 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.

## Note

The sums of each row of the input tridiagonal matrix should be 0.

`eff.ini.seceig.general` for the general conservative matrix next to the maximal eigenpair.
 ```1 2 3 4 5 6``` ```a = c(1:7)^2 b = c(1:7)^2 eff.ini.seceig.tri(a, b, xi = 0) eff.ini.seceig.tri(a, b, xi = 1) eff.ini.seceig.tri(a, b, xi = 2/5) ```