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This paper is concerned with mathematical, computational, and historical aspects of the Chinese Remainder and Interpolation Theorems of number theory and numerical analysis, with a view to their application to symbolic computation.
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)
In the past decade the Cooley-Tukey fast Fourier transform (FFT)  has achieved the status of a “super” algorithm. As a numerical (complex field) algorithm, the FFT has revolutionized large scale time series analysis in a way that counts most—economic. (See, e.g., Refs. 3-6.) Since the late sixties, the FFT has also emerged as an… (More)