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# NP-Incompleteness

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## Levinson Recursion

20 Feb 2021

Norman Levinson was an American mathematician, son of Russian Jewish immigrants and grew up poor. He eventually enrolled at MIT and majored in Electrical Engineering but switched to Mathematics during his PhD in no small part due to Norbert Wiener.

Levinson spent two years at the Institute for Advanced Study at Princeton where we has supervised by von Neumann. During the Great Depression, Levinson applied to a position at MIT and was initially refused, likely due to anti-semitic discrimination. The famous British mathematician G. H. Hardy intervened and is reported to have said to the university’s provost, Vannevar Bush:

Tell me, Mr Bush, do you think you’re running an engineering school or a theological seminary? Is this the Massachusetts Institute of Theology? If it isn’t, why not hire Levinson.

Levinson got the job in 1937 but almost lost it during the McCarthy era due to an initial association with the American Communist Party. Levinson passed away in 1975 [1].

In this post we’ll discuss the Levinson Recursion algorithm, also known as Levinson–Durbin recursion, which can be used to solve the equation $A x = y$ more efficiently if $A$ obeys some specific properties.