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Approximate complex polynomial evaluation in near constant work per point

Published: 04 May 1997 Publication History
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References

[1]
A.V. Aho, J.E. Hopcroft, J.D. Ullman, The Design and Analysis of Computer Algorithms, Addison Wesley (1974).
[2]
A.V. Aho, K. Steiglitz, and J.D. Ullman, Evaluating Polynomials at Fixed Set of Points, SIAM J. on Computing 4 (1975), 533-539.
[3]
Bini D., Pan V., Polynomial and Matrix Computations, Volume I, Birkhauser,Boston, MA, (1994).
[4]
A.B. Borodin and I. Munro, Evaluating polynominals at many points, Information Processing Letters 1:2 (1971), 66-68.
[5]
A.B. Borodin and I. Munro, The Computational Complexity of Algebraic and Numerical Problems, American Elsevier, New York (1975).
[6]
P.B. Callahan and S.R. Kosaraju, A decomposition of multi-dimensional point sets with applications to k-nearest-neighbors and n-body potential fields, J. ACM 42:1 (1995), 67-90.
[7]
J. Carrier, L. Greengard, and V. Rokhlin, A fast adaptive Multipole algorithm for particle simulations, SiAM J. Scientific and Statistical Computing 9:4 (1988), 669-686.
[8]
C.D. Conte and C. deBoor, Elementary Numerical Analysis: An Algorithmic Approach, McGraw- Hill, NY (1980).
[9]
j.M. Cooley, P.A. Lewis, and P.D. Welch, History of the fast Fourier transform, Proc. IEEE 55 (1967), 1675-1677.
[10]
J.M. Cooley and J.W. Tukey, An algorithm for the machine calculation of complex Fourier series, Math. Comp. 19 (1965), 297-301.
[11]
G. Dahlquist and A. BjSrck, Numerical Methods, Prentice-Hall, Englewood Cliffs, NJ (1974).
[12]
G.C. Danielson and C. Lanczos, Some improvements in practical Fourier analysis and their application to X-ray scattering from liquids, J. Franklin Institute 233 (1942), 365-380 and 435- 452.
[13]
A.L. Delcher and S.R. Kosaraju, Optimal parallel evaluation of tree-structured computations by raking, Proc. 3rd Aegean Work. on Comp. (1988), 101-110.
[14]
A. Dutt, M. Gu, V. Rokhlin, Fast Algorithms for Polynomial Interpolation, integration and Differentiation, SIAM J. Numer. Anal., Vol. 33,No. 5, (1996), 1689-1711
[15]
A. Dutt, Fast Fourier Transforms for Nonequispaced Data, Yale Department of Computer Science, Technical Report 980, (1993).
[16]
A. Dutt, V. Rokhlin, Fast Fourier Transforms for Nonequispaced Data II, Applied and Computational Harmonic Analysis, Acedemic Press, 2, (1995), pp. 85-100.
[17]
A. Edelman, P. McCorquodale, S. Toledo, The Future Fast Fourier Transform?, Eighth SIAM Conference on Parallel Processing, Minneapolis, MN, March (1997).
[18]
W.D. Elliott and J.A. Board, Fast fourier transform accelerated fast multipole algorithm, SIAM J. Sci. Comput., Vol. 17, No. 2 (1996), 398-415.
[19]
C.M. Fiduccia, Polynomial evaluation via the division algorithm- the fast Fourier transform revisited, Proc. 4th Annual ACM Symposium on Theory of Computing (1972), 88-93.
[20]
W.M. Gentleman and G. Sande, Fast Fourier transforms for fun and profit, Proc. AFIPS 1966 Fall Joint Computer Conf. 29 (1966), 563-578.
[21]
A. Gerasoulis, A Fast Algorithm for the Multiplication of Generalized Hilbert Matrices with Vectors, Math. of Computation 50:t81 (1988), 179-188.
[22]
A. Gerasoulis, M.D. Grigoriadis, and Liping Sun, A fast algorithm for Trummer's problem, SIAM J. Sci. Statist. Comput. 8 (1987), 135-138.
[23]
I.J. Good, The interaction algorithm and practical Fourier series, J. Royal Statistics Soc. B20 (1958), 361-372. Addendum 22 (1960), 372-375.
[24]
L. Greengard and V. Rokhlin, A fast algorithm for particle simulations, J. Computational Physics 73 (1987), 325-348.
[25]
L. Greengard and V. Rokhlin, On the efficient implementation of the fast multipole algorithm, TR RR-602, Yale Univ. Dept. of CS, (1988).
[26]
P. Henrici, Applied and Computational Complex Analysis, III, Wiley, New York (1986).
[27]
M.S. Henry, Approximation by Polynomials: Interpolation and Optimal Nodes, Math. Monthly 91:8 (1984), 497-499.
[28]
E. Horowitz, A fast method for interpolation using preconditioning, Information Processing Letters 1:4 (1972), 157-163.
[29]
H.T. Kung, Fast evaluation and interpolation, Dept. of Comp. Sci., Carnegie-Mellon Univ., Pittsburgh, PA. (1973).
[30]
G.L. Miller and J.H. Reif, Parallel tree contraction part 1: Fundamentals, Chapter in Randomness and Computation S. Micali, Ed. 5 JAi Press, Greenwich, CT (1989), 47-72.
[31]
R. Moenck and A.B. Borodin, Fast modular transforms via division, Conf. Record, IEEE 13th Annual Symp. on Switching and Automata Theory (i972), 90-96.
[32]
A.C.R. Newbery, Error Analysis for Polynomial Evaluation, Math. Comp. 28:127 (197'9), 789-793.
[33]
V. Pan, Fast Evaluation and Interpolation at the Chebyshev Sets of Points, Appl. Math. Lett. 2:3 ( 1989 ), 255- 258.
[34]
V.Y. Pan, J.H. Reif, and S.R. Tate, The Power of Combining the Techniques of Algebraic and Numerical Computing: Improved Approximate Multipoint Polynomial Evaluation and Improved Multipole Algorithms, Proc. 32nd Ann. IEEE Syrup. Foundations of Computer Science, Pittsburgh, PA (1992), 703-713.
[35]
V. Pan, A. Sadikou, E. Landowne, and O. Tiga, A New Approach to Fast Polynomial Interpolation and Multipoint Evaluation, to appear (1996).
[36]
L.R. Rabiner and C.M. Ra~er (eds.), Digital Signal Processing, IEEE Press, New York (1972).
[37]
J.H. Reif, Approximate Complex Polynomial Evaluation in Near Constant Work Per Point, full version of this paper, in postscript (1997). http://www.cs, d u ke. ed u / ^- reiff paper/Eval, ps
[38]
J.H. Reif and S.R. Tate, Fast spatial decomposition and closest pair computation for limited precision input., Tech. Rpt. No96-001, Univ. of North Texas, Dept. of Computer Science (1996). http: / / www.cs.duke.ed u/,~reif/paper / Sep.ps
[39]
J.H. Reif and S.R. Tale, N-body simulation I: Fast algorithms for potential field evaluation and 7)-ummer's problem, Tech. Rpt. N-96-002, Univ. of North Texas, Dept. of Computer Science (1996). http://www.cs.duke.edu/~,reif/paper/Multipole.ps
[40]
V. Rokhlin, A Fast Algorithm for the Discrete Laplace transformation, J. of Complexity 4 (1988), 12-32.
[41]
C. Runge and H. KSnig, Die Grundlehren der mathematischen Wissenschaften, 11 (1924), Springer, Berlin.

Cited By

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  • (2010)An Efficient Method for Evaluating Complex PolynomialsJournal of Signal Processing Systems10.1007/s11265-008-0265-858:1(17-27)Online publication date: 1-Jan-2010
  • (2007)A fully-pipelined parallel architecture for Kalman tracking filterProceedings of the 2007 IEEE International Conference on Application-Specific Systems, Architectures and Processors10.1109/ASAP.2007.4429968(81-86)Online publication date: 9-Jul-2007
  • (2005)Transformations of Cauchy matrices, Trummer's problem and a Cauchy-like linear solverSolving Irregularly Structured Problems in Parallel10.1007/BFb0018546(274-284)Online publication date: 9-Jun-2005
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cover image ACM Conferences
STOC '97: Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
May 1997
752 pages
ISBN:0897918886
DOI:10.1145/258533
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 04 May 1997

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Cited By

View all
  • (2010)An Efficient Method for Evaluating Complex PolynomialsJournal of Signal Processing Systems10.1007/s11265-008-0265-858:1(17-27)Online publication date: 1-Jan-2010
  • (2007)A fully-pipelined parallel architecture for Kalman tracking filterProceedings of the 2007 IEEE International Conference on Application-Specific Systems, Architectures and Processors10.1109/ASAP.2007.4429968(81-86)Online publication date: 9-Jul-2007
  • (2005)Transformations of Cauchy matrices, Trummer's problem and a Cauchy-like linear solverSolving Irregularly Structured Problems in Parallel10.1007/BFb0018546(274-284)Online publication date: 9-Jun-2005
  • (1998)Approximate polynomial Gcds, Padé approximation, polynomial zeros and bipartite graphsProceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms10.5555/314613.314649(68-77)Online publication date: 1-Jan-1998

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