R. Moenck and A. B. Borodin, "Fast modular transforms via division," in Conf. Record, IEEE 13th Annual Symp. on Switching and Automata Theory ~IEEE Press, Piscataway, N.J., 1972!, pp. 90 --96. Home/Search Document Not in Database Summary Related Articles Check |
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Fast Multiplication And Its Applications - Bernstein (Correct)
....for the division of two polynomials with remainder. I have not attempted to trace the earlier history of the x valuation. Improvements. Another way to divide h by f is to recursively divide the top half of h by the top half of f , then recursively divide what s left. Moenck and Borodin in [74] published this algorithm (in the polynomial case) and observed that it lg lg n) Unfortunately, Borodin and Moenck omitted the algorithm from [19] apparently believing that the extra lg n factor removed it from competition. This belief has not been adequately investigated. Many years later, ....
....and nonzero integers f 1 ; f 2 ; f t , computes integers r 1 ; r 2 ; r t , with 0 r j jf j j, such that h is congruent modulo f j to r j . The algorithm takes lg lg n) where n is the total number of input bits. History. This algorithm was published by Borodin and Moenck in [74] and [19, Sections 4 6] for single precision moduli f 1 ; f 2 ; f t . Improvements. The computation of reciprocals, as described in Section 6, can be sped up inside this application. Consider, for example, dividing by f 1 f 2 , then by f 1 , then by f 2 . Section 6 computes approximate ....
Robert T. Moenck, Allan Borodin, Fast modular transforms via division, in [57] (
Relax, But Don't Be Too Lazy - van der Hoeven (2000) (Correct)
....formal power series, polynomials, and integers. Indeed, 3 http: algo.inria.fr libraries software.html 52 Relax But Don t Be Too Lazy one of the by products of Joris van der Hoeven s report is a division algorithm with remainder in K(n) operations, whereas the best known algorithm was in 2K(n) [7, 2, 5]. Related work. For truncated division and square root, new algorithms based on Karatsuba s multiplication are detailed in the report [4] Acknowledgement. People who don t read French may thank Gina Pierrel ee Grisvard who helped to translate this summary. ....
Moenck (R.) and Borodin (A.). { Fast modular transforms via division. In Proceedings of the 13th Annual IEEE Symposium on Switching and Automata Theory, pp. 90-96. { October 1972.
Approximate Complex Polynomial Evaluation In Near Constant Work.. - Reif (1999) (1 citation) (Correct)
.... multipoint complex (real) polynomial evaluation and interpolation problems restrict D to the complex numbers C (real numbers R, respectively) Exact algorithms for multipoint polynomial evaluation and interpolation use modular techniques developed in the initial work of Moenck and Borodin [27], Borodin and Munro [4] Horowitz [25] Fiduccia [16] and Kung [26] and were improved by Borodin and Munro [5] to the best known work bounds: O( n m) log 2 (n m) for evaluation and O(n log 2 n) for interpolation. An error analysis for these algorithms is given by Newbery [28] Pan et al. ....
....for each k = 0, m 1. Then for each j = 0, #n m# 1 we do the multipoint evaluation P j (z k ) for k = 0, m 1 and also compute each z jm k by multiplication of z m k times z (j 1)m k . By application of Proposition 1. 1, combined with previous exact algorithms [27, 16, 26, 5] for m point polynomial evaluation for #n m# polynomials of degree m 1, which require work O(m log 2 m) each, we have the m point polynomial evaluation problem, for m # n, which can be computed within work #n m#(m log 2 m) # O(n log 2 m) Also, the multipoint polynomial evaluation ....
R. Moenck and A. B. Borodin, Fast modular transforms via division, in Conf. Record, IEEE 13th Ann. Symposium on Switching and Automata Theory, 1972, pp. 90--96.
Efficient Parallel Algorithms for Optical Computing - With The Discrete (Correct)
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R. Moenck and A. B. Borodin, "Fast modular transforms via division," in Conf. Record, IEEE 13th Annual Symp. on Switching and Automata Theory ~IEEE Press, Piscataway, N.J., 1972!, pp. 90 --96.
How To Find Small Factors Of Integers - Bernstein (2000) (2 citations) (Correct)
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Robert T. Moenck, Allan Borodin, Fast modular transforms via division, in [93] (1972), 90-96.
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