List of Direct Algorithms

4.2   QR algorithm for HEP   

4.2   Divide-and-conquer algorithm for HEP   

4.2   Bisection method and inverse for HEP   

4.2   Inverse iteration for HEP   

4.2   Relatively robust representation algorithm for HEP   

5.3   QR algorithm for GHEP   

5.3   Divide-and-conquer algorithm for GHEP   

5.3   Bisection method and inverse iteration for GHEP   

6.2   QR algorithm for SVD   

6.2   Divide-and-conquer QR algorithm for SVD   

6.2   DQDS algorithm for SVD   

6.2   Bisection method and inverse iteration for SVD   

7.3   QR algorithm for NHEP   

8.2   QZ algorithm for GNHEP   

8.2   GUPTRI algorithm for GNHEP of singular pencils   

Note that a direct algorithm must still iterate, since finding eigenvalues is mathematically equivalent to finding zeros of polynomials, for which no noniterative methods can exist. We call a method direct if experience shows that it (nearly) never fails to converge in a fixed number of iterations.