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The Hessenberg decomposition of a general matrix will produce a similar matrix in upper Hessenberg form at the cost of ~ $\cfrac{10}{3}n^3$ flops. However, if the matrix is Symmetric/Hermitian, the Hessenberg decomposition will result in a similar tridiagonal matrix and the symmetry can be exploited to compute this in ~ $\cfrac{4}{3}n^3$ which is less than half that of the general case. As such, a specialized algorithm should be added to the Hessenberg decomposition for the symmetric case.
A pseudocode implementation from Fundamentals of matrix computation (David S Watkins) is provided as reference.
The text was updated successfully, but these errors were encountered:
The Hessenberg decomposition of a general matrix will produce a similar matrix in upper Hessenberg form at the cost of ~$\cfrac{10}{3}n^3$ flops. However, if the matrix is Symmetric/Hermitian, the Hessenberg decomposition will result in a similar tridiagonal matrix and the symmetry can be exploited to compute this in ~ $\cfrac{4}{3}n^3$ which is less than half that of the general case. As such, a specialized algorithm should be added to the Hessenberg decomposition for the symmetric case.
A pseudocode implementation from Fundamentals of matrix computation (David S Watkins) is provided as reference.
![symmHess](https://user-images.githubusercontent.com/47160062/233799991-5621cce8-b6d0-4b0a-9e61-d7043d5f74f9.png)
The text was updated successfully, but these errors were encountered: