Abstract

Perhaps, the most astonishing idea in eigenvalue computation is Rutishauser's idea of applying the LR transform to a matrix for generating a sequence of similar matrices that become more and more triangular. The same idea is the foundation of the ubiquitous QR algorithm. It is well known that this idea originated in Rutishauser's qd algorithm, which precedes the LR algorithm and can be understood as applying LR to a tridiagonal matrix. But how did Rutishauser discover qd and when did he find the qd–LR connection? We checked some of the early sources and have come up with an explanation.

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