ZHPGV Example

To find all the eigenvalues and eigenvectors of the generalized Hermitian eigenproblem Ax = $\lambda$Bx, where

A = $$\left(\vphantom{ \begin{array}{cccc} -7.36 & 0.77 - 0.43i & -0.... ... \\ 3.01 + 6.97i & 1.90 - 3.73i & 2.88 + 3.17i & -2.54 \end{array} }\right.$$$$\begin{array}{cccc} -7.36 & 0.77 - 0.43i & -0.64 - 0.92i & 3.01 ... ...8 - 3.17i \\ 3.01 + 6.97i & 1.90 - 3.73i & 2.88 + 3.17i & -2.54 \end{array}$$$$\left.\vphantom{ \begin{array}{cccc} -7.36 & 0.77 - 0.43i & -0.... ... \\ 3.01 + 6.97i & 1.90 - 3.73i & 2.88 + 3.17i & -2.54 \end{array} }\right)$$

and

B = $$\left(\vphantom{ \begin{array}{cccc} 3.23 & 1.51 - 1.92 i & 1.9... ... 0.42 - 2.50 i & -1.18 - 1.37 i & 2.33 + 0.14 i & 4.29 \end{array} }\right.$$$$\begin{array}{cccc} 3.23 & 1.51 - 1.92 i & 1.90 + 0.84 i & 0.42 ... ...0.14 i \\ 0.42 - 2.50 i & -1.18 - 1.37 i & 2.33 + 0.14 i & 4.29 \end{array}$$$$\left.\vphantom{ \begin{array}{cccc} 3.23 & 1.51 - 1.92 i & 1.9... ... 0.42 - 2.50 i & -1.18 - 1.37 i & 2.33 + 0.14 i & 4.29 \end{array} }\right)$$,

together with an estimate of the condition number of B, and approximate error bounds for the computed eigenvalues and eigenvectors.

The example program for ZHPGVD illustrates solving a generalized symmetric eigenproblem of the form ABx = $\lambda$x.

Example program
Example data
Example results