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The Computation Of Eigenvalues And Eigenvectors Of An Nxn Real General Matrix, Yeh-Hao Ma
The Computation Of Eigenvalues And Eigenvectors Of An Nxn Real General Matrix, Yeh-Hao Ma
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
The eigenvalues of the matrix eigenproblem Ax = λx are computed by the QR double-step method and the eigenvectors by inverse power method.
The matrix A is preliminarily scaled by the equilibration and normalization procedure. The scaled matrix is then reduced to an upper-Hessenberg form by Householder's method. The QR double-step iteration is performed on the upper-Hessenberg matrix. After all the eigenvalues are found, the inverse power method is performed on the upper-Hessenberg matrix to obtain the corresponding eigenvectors.
The program consists of five subroutines which is able to find real and/or complex eigen value/vector of an nxn real matrix.