John D. Lipson

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The analytic concepts of approximation, convergence, differentiation, and Taylor series expansion are applied and interpreted in the context of an abstract power series domain. Newton's method is then shown to be applicable to solving for a power series root of a polynomial with power series coefficients, resulting in fast algorithms for a variety of power(More)
This is the second in a series of two tutorial sessions featuring letures from the 1975-76 SIGSAM Lecture Program. Prof. Lipson's tutorial will discuss the Cooley-Tukey fast Fourier transform, and algorithm which has truly revolutionized large scale time series analysis. Prof. Horowitz presents a taxonomy of algorithms with examples of algorithms in each(More)
It is possible to construct polynomials a(x), b(r) of the type required (i.e., of degree 4~ 1 with all coeflicients fl) such that f(z) = G&,+,~~, g(s) = @.2pl@z. The construction is illustrated below for the case n= 18. If 2m is the highest power of 2 dividing n, there are at most m + 1 cyclically orthogonal vectors of length n with coordinates fl (without(More)
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