Bibliography for the Jenkins-Traub Method

short

 

  1. A constructive algorithm for finding the exact roots of polynomials with computable real coefficients. Real numbers.  
    Lester, David; Chambers, Scott; Lu, Heoi Lee
    Theoret. Comput. Sci.  279  (2002),  no. 1-2, 51--64, MathSciNet.
  2. A New Iterative Method for the Computation of the Solutions of Nonlinear Equations
    Costabile F.; Gualtieri M.I.; Luceri R.
    Numerical Algorithms, December 2001, vol. 28, no. 1-4, pp. 87-100(14), Ingenta.
  3. Solving a Polynomial Equation: Some History and Recent Progress  
    Victor Y. Pan  
    SIAM Review, Vol. 39, No. 2. (Jun., 1997), pp. 187-220, Jstor.  
  4. Polynomial Roots from Companion Matrix Eigenvalues  
    Alan Edelman; H. Murakami  
    Mathematics of Computation, Vol. 64, No. 210. (Apr., 1995), pp. 763-776, Jstor.  
  5. Polynomial root finding
    Lang, Markus; Frenzel, Bernhard-Christian  
    IEEE Signal Processing Letters, v 1, n 10, Oct, 1994, p 141-143, Compendex.
  6. Some complexity results for zero finding for univariate functions.
    Novak, Erich; Ritter, Klaus
    Festschrift for Joseph F. Traub, Part I.  J. Complexity  9  (1993),  no. 1, 15--40, MathSciNet.
  7. A modified fast Fourier transform for polynomial evaluation and the Jenkins-Traub algorithm.  
    Hager, William W.
    Numer. Math.  50  (1987),  no. 3, 253--26, MathSciNet.
  8. ANewton's Method and the Jenkins-Traub Algorithm  
    R. N. Pederson  
    Proceedings of the American Mathematical Society, Vol. 97, No. 4. (Aug., 1986), pp. 687-690, Jstor.  
  9. A Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients  
    I. J. Schoenberg  
    The American Mathematical Monthly, Vol. 93, No. 1. (Jan., 1986), pp. 8-13, Jstor.  
  10. Divided Differences, Shift Transformations and Larkin's Root Finding Method  
    A. Neumaier; A. Schafer  
    Mathematics of Computation, Vol. 45, No. 171. (Jul., 1985), pp. 181-196, Jstor.  
  11. A parallel algorithm for simple roots of polynomials.
    Ellis, George H.; Watson, Layne T.
    Comput. Math. Appl. 10 (1984), no. 2, 107--121, MathSciNet.
  12. Algorithms for solvents of matrix polynomials  
    J.E. Dennis, J.F. Traub and R.P. Weber  
    SIAM J. Numer. Anal. 15 (1978) 523--533.
  13. A Generalization of the Jenkins-Traub Method  
    J. A. Ford  
    Mathematics of Computation, Vol. 31, No. 137. (Jan., 1977), pp. 193-203, Jstor.  
  14. Study Of Techniques For Finding The Zeros Of Linear Phase Fir Digital Filters
    Schmidt, C. E.; Rabiner, L. R.
    IEEE Transactions on Acoustics, Speech, and Signal Processing, v ASSP-25, n 1, Feb, 1977, p 96-97, Compendex.
  15. The algebraic theory of matrix polynomials  
    J.E. Dennis, J.F. Traub and R.P. Weber  
    SIAM J. Numer. Anal. 13 (1976) 831--845.
  16. Algorithm 493: zeros of a real polynomial
    M.A. Jenkins
    ACM Trans. Math. Software 1 (1975) 178--179.
  17. Calculation of Zeros of a Real Polynomial Through Factorization Using Euclid's Algorithm  
    Donna K. Dunaway  
    SIAM Journal on Numerical Analysis, Vol. 11, No. 6. (Dec., 1974), pp. 1087-1104, Jstor.  
  18. Root Estimators (in Theory and Methods)  
    O. C. Jenkins; L. J. Ringer; H. O. Hartley  
    Journal of the American Statistical Association, Vol. 68, No. 342. (Jun., 1973), pp. 414-419, Jstor.  
  19. Algorithm 419: Zeros of a complex polynomial  
    M.A. Jenkins and J.F. Traub
    Comm. ACM 15 (1972) 97--99.
  20. The Numerical Factorization of a Polynomial  
    A. S. Householder; G. W. Stewart  
    SIAM Review, Vol. 13, No. 1. (Jan., 1971), pp. 38-46, Jstor.  
  21. On optimum root-finding algorithms.  
    Rissanen, J.
    J. Math. Anal. Appl.  36  1971 220--225, MathSciNet.
  22. A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration  
    M. A. Jenkins; J. F. Traub  
    SIAM Journal on Numerical Analysis, Vol. 7, No. 4. (Dec., 1970), pp. 545-566, Jstor.  
  23. A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration  
    M.A. Jenkins and J.F. Traub,
    Numer. Math. 14 (1970) 252--263.
  24. The advantages and disadvantages in using complex arithmetic in polynomial zerofinding  
    M.A. Jenkins
    Proc. Fourth Annual Princeton Conf. on Information Science and Systems, Dept. Electr. Engrg., Princeton Univ., NJ (1970) 129--132.
  25. An algorithm for an automatic general polynomial solver  
    M.A. Jenkins and J.F. Traub; B. Dejon and P. Henrici, Eds.
    Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969) 151--180.
  26. Some iterations for factoring a polynomial.
    Stewart, G. W.
    Numer. Math. 13 1969 458--470, MathSciNet.
  27. Constructive aspects of the fundamental theorem of algebra.
    Edited by Bruno Dejon and Peter Henrici
    Proceedings of a Symposium Conducted at the IBM Research Laboratory, Zürich-Rüschlikon, June 5-7, 1967. Wiley-Interscience A Division of John Wiley & Sons, Ltd., London-New York-Sydney 1969 vii+337 pp., MathSciNet.
  28. Some iterations for factoring a polynomial.
    Stewart, G. W.
    Numer. Math. 13 1969 458--470, MathSciNet.
  29. On Newton-Raphson Iteration (in Classroom Notes)  
    J. F. Traub  
    The American Mathematical Monthly, Vol. 74, No. 8. (Oct., 1967), pp. 996-998, Jstor.  
  30. The calculation of zeros of polynomials and analytic functions  
    J. Traub
    Mathematical Aspects of Computer Science, Proc. Sympos. Appl. Math. 19 (Amer. Mathematical Soc., Providence, RI, 1967) 138--152.
  31. Iteration functions for solving polynomial matrix equations.
    Pavel-Parvu, Monica; Korganoff, André
    Constructive Aspects of the Fundamental Theorem of Algebra (Proc. Sympos., Zürich-Rüschlikon, 1967)  pp. 225--280, Wiley-Interscience, New York, MathSciNet.
  32. Associated Polynomials and Uniform Methods for the Solution of Linear Problems  
    J. F. Traub  
    SIAM Review, Vol. 8, No. 3. (Jul., 1966), pp. 277-301, Jstor.  
  33. Proof of global convergence of an iterative method for calculating complex zeros of a polynomial  
    J.F. Traub  
    Notices Amer. Math. Soc. 13 (1966) 117.
  34. A class of globally convergent iteration functions for the solution of polynomial equations  
    J.F. Traub  
    Math. Comp. 20 (1966) 113--138.
  35. A class of globally convergent iteration functions for the solution of polynomial equations  
    J.F. Traub
    Proc. IFIP Congress 65, 2 (Spartan Books, Washington, DC, 1965) 483--484.
  36. Construction of globally convergent iteration functions for the solution of polynomial equations  
    J.F. Traub  
    Bull. Amer. Math. Soc. 71 (1965) 894--895.
  37. Iterative methods for the solution of equations  
    Traub, J. F.
    Prentice-Hall Series in Automatic Computation Prentice-Hall, Inc., Englewood Cliffs, N.J. 1964 xviii+310 pp., MathSciNet.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005