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Improve reductions to bi- and tridiagonal matrices #66

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andreasnoack opened this issue May 7, 2020 · 0 comments
Open

Improve reductions to bi- and tridiagonal matrices #66

andreasnoack opened this issue May 7, 2020 · 0 comments

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@andreasnoack
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andreasnoack commented May 7, 2020 •
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The current versions are very basic and pretty slow compared to LAPACK. They should at a minimum be blocked but we should also consider the methods described in https://books.google.dk/books?hl=en&lr=&id=bx7pAwAAQBAJ&oi=fnd&pg=PA135&dq=Sergey+V+Kuznetsov+bidiagonal&ots=U0trQWuG9j&sig=cGZDU36MrBCKNqRp4V4b1w_55M0&redir_esc=y#v=onepage&q=Sergey%20V%20Kuznetsov%20bidiagonal&f=false and reference [5]. We might even make them run in parallel and be faster vanilla LAPACK.

The right place to start testing these would be the QR factorization. The idea is the same but the QR is much simpler.
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