# EfficientMaxEigenpair: EfficientMaxEigenpair: A package for computating the maximal... In EfficientMaxEigenpair: Efficient Initials for Computing the Maximal Eigenpair

## Description

The EfficientMaxEigenpair package provides some auxillary functions and five categories of important functions: `tridiag`, `tri.sol`, `find_deltak`, `ray.quot.tri`, `shift.inv.tri`, `ray.quot.seceig.tri`, `ray.quot.general`, `ray.quot.seceig.general`, `eff.ini.maxeig.tri`, `eff.ini.maxeig.shift.inv.tri`, `eff.ini.maxeig.general`, `eff.ini.seceig.tri` and `eff.ini.seceig.general`.

## EfficientMaxEigenpair functions

`tridiag`: generate tridiagonal matrix Q based on three input vectors.

`tri.sol`: construct the solution of linear equation (-Q-zI)w=v.

`find_deltak`: compute δ_k for given vector v and matrix Q.

`ray.quot.tri`: rayleigh quotient iteration algorithm to computing the maximal eigenpair of tridiagonal matrix Q.

`shift.inv.tri`: shifted inverse iteration algorithm to computing the maximal eigenpair of tridiagonal matrix Q.

`ray.quot.seceig.tri`: rayleigh quotient iteration algorithm to computing the next to maximal eigenpair of tridiagonal matrix Q.

`ray.quot.general`: rayleigh quotient iteration algorithm to computing the maximal eigenpair of general matrix A.

`ray.quot.seceig.general`: rayleigh quotient iteration algorithm to computing the next to maximal eigenpair of general matrix A.

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

`eff.ini.maxeig.shift.inv.tri`: calculate the maximal eigenpair for the tridiagonal matrix by shifted inverse iteration algorithm.

`eff.ini.maxeig.general`: calculate the maximal eigenpair for the general matrix.

`eff.ini.seceig.tri`: calculate the next to maximal eigenpair for the tridiagonal matrix whose sums of each row should be 0.

`eff.ini.seceig.general`: calculate the next to maximal eigenpair for the general conservative matrix.

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