The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Inverses of Multivariable Polynomial Matrices by Discrete Fourier Transforms
Multidimensional Systems and Signal Processing
On the computation of the inverse of a two-variable polynomial matrix by interpolation
Multidimensional Systems and Signal Processing
On the Newton bivariate polynomial interpolation with applications
Multidimensional Systems and Signal Processing
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In the past decade the Cooley-Tukey fast Fourier transform (FFT) [1] 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 important algebraic(abstract field) algorithm, with many interesting applications to the theory and practice of algebraic computing. The abstract character of the FFT, in particular its role as an algebraic algorithm, is what this paper is about. Our discussion centres around the following questions: 1. What is the discreteFourier transform? 2. What is the fastFourier transform? 3. What is its role in algebraiccomputing? 4. Is a finite field(mod p) FFT feasible?