What Hadamard Missed,
CALIFORNIA UNIV BERKELEY CENTER FOR PURE AND APPLIED MATHEMATICS
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Consider the task of finding all the eigenvalues of a dense matrix. We show how Hadamards procedure 1891 can be organized into Aitkens H-table 1925 and how the H-table may be transformed into Rutishausers qd-array 1953 with the help of the Lanczos algorithm. We show how the qd algorithm can be interpreted as defining the LR algorithm 1958. Finally we show how the original qd algorithm may be transformed into the shifted differential qd algorithm dqds developed by Fernando and Parlett 199394. The Lanczos algorithm takes a dense matrix into tridiagonal form and then dqds is a fast and accurate procedure for extracting the eigenvalues.
- Numerical Mathematics