Reasoning with the infinite: From the closed world to the mathematical universe: By Michel Blay (Translated by M. B. DeBevoise). University of Chicago Press, Chicago. (1998). 216 pages. $30.00; £25.95
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 100 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0898-1221
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✦ Synopsis
Computational number theory. Thoughts on Part I. 2. Computational number theory. 3. Polynomial algebra. 4. Theoretical aspects of the discrete Fourier transform and convolution. 5. Cyclotomic polynomial factorization and associated fields. 6. Cyclotomic polynomial factorization in finite fields. 7. Finite integer rings: Polynomial algebra and cyclotomic facorization. II. Convolution algorithms. Thoughts on Part II. 8. Fast algorithms for acyclic convolution. 9. Fast one-dimensional cyclic convolution algorithms. 10. Two-and higher-dimensional cyclic convolution algorithms. 11. Validity of fast algorithms over different number systems. 12. Fault tolerance for integer sequences. III. Fast Fourier transform (FFT) algorithms. Thoughts on Part III. 13. Fast Fourier transform: One-dimensional data sequences. 14. Fast Fourier transform: Multidimensional data sequences. IV. Recent results on algorithms in finite integer rings. Thoughts on Part IV. Paper one: A number theoretic approach to fast algorithms for two-dimensional digital signal processing in finite integer rings. Paper two: On fast algorithms for one-dimensional digital signal processing in finite integer and complex integer rings. Paper three: Cyclotomic polynomial factorization in finite integer rings with applications to digital signal processing. Paper four: Error control techniques for data sequences defined in finite integer rings. Appendices. A. Small length acyclic convolution algorithms. B. Classification of cyclotomic polynomials. Index.