Jenkins--Traub method

A.D. Booth, Numerical Methods (Butterworth, London, 1955).

L. Brand, Applications of the companion matrix, Amer. Math. Monthly 75 (1968) 146--152.

L. Brand, The companion matrix and its properties, Amer. Math. Monthly 71 (1964) 629--634.

B.W. Char, Floating point isolation of zeros of a real polynomial via MACSYMA, in: Proc. of the 1977 MACSYMA Users' Conference, U.S. Govt. Printing Office (1978) 53--54.

S.P. Chung, An algorithm for the zeros of transcendental functions, Numer. Math. 32 (1979) 359--371.

S.P. Chung, Generalization and acceleration of an algorithm of Sebastião e Silva and its duals, Numer. Math. 25 (1976) 365--377.

J.E. Dennis, J.F. Traub and R.P. Weber, Algorithms for solvents of matrix polynomials, SIAM J. Numer. Anal. 15 (1978) 523--533.

J.E. Dennis, J.F. Traub and R.P. Weber, The algebraic theory of matrix polynomials, SIAM J. Numer. Anal. 13 (1976) 831--845.

W.W. Hage, A modified fast Fourier transform for polynomial evaluation and the Jenkins--Traub algorithm, Numer. Math. 50 (1987) 253--261.

A.S. Householder and G.W. Stewart, The numerical factorization of a polynomial, SIAM Rev. 13 (1971) 38--46.

A.S. Householder, Multigradients and the zeros of transcendental functions, Linear Algebra Appl. 4 (1971) 175--182.

A.S. Householder, Schröder and Trudi: A historical excursion, SIAM Rev. 16 (1974) 344--348.

A.S. Householder and G.W. Stewart, Comments on "Some iterations for factoring polynomials", Numer. Math. 13 (1969) 470--471.

M.A. Jenkins, The advantages and disadvantages in using complex arithmetic in polynomial zerofinding, in: Proc. Fourth Annual Princeton Conf. on Information Science and Systems, Dept. Electr. Engrg., Princeton Univ., NJ (1970) 129--132.

M.A. Jenkins and J.F. Traub, A three-stage variable-shift iteration for polynomial zeros and its relation to generalized Rayleigh iteration, Numer. Math. 14 (1970) 252--263.

M.A. Jenkins, Algorithm 493: zeros of a real polynomial, ACM Trans. Math. Software 1 (1975) 178--179.

M.A. Jenkins and J.F. Traub, An algorithm for an automatic general polynomial solver, in: B. Dejon and P. Henrici, Eds., Constructive Aspects of the Fundamental Theorem of Algebra (Wiley/Interscience, New York, 1969) 151--180.

M.A. Jenkins and J.F. Traub, A three-stage algorithm for real polynomials using quadratic iteration, SIAM J. Numer. Anal. 7 (1970) 545--566.

M.A. Jenkins and J.F. Traub, Algorithm 419: Zeros of a complex polynomial, Comm. ACM 15 (1972) 97--99.

R.N. Pederson, Newton's method and the Jenkins--Traub algorithm, Proc. Amer. Math. Soc. 97 (1986) 687--690.

A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis (McGraw-Hill, New York, 2nd ed., 1987) 354.

C.E. Schmidt and L.R. Rabiner, A study of techniques for finding the zeros of linear phase FIR digital filters, IEEE Trans. Acoust. Speech Signal Process. 25 (1977) 96--98.

G.W. Stewart, Some iterations for factoring a polynomial, Numer. Math. 13 (1969) 458--471.

J. Traub, The calculation of zeros of polynomials and analytic functions, in: Mathematical Aspects of Computer Science, Proc. Sympos. Appl. Math. 19 (Amer. Mathematical Soc., Providence, RI, 1967) 138--152.

J.F. Traub, Proof of global convergence of an iterative method for calculating complex zeros of a polynomial, Notices Amer. Math. Soc. 13 (1966) 117.

J.F. Traub, A class of globally convergent iteration functions for the solution of polynomial equations, Math. Comp. 20 (1966) 113--138.

J.F. Traub, A class of globally convergent iteration functions for the solution of polynomial equations, in: Proc. IFIP Congress 65, 2 (Spartan Books, Washington, DC, 1965) 483--484.

J.F. Traub, Construction of globally convergent iteration functions for the solution of polynomial equations, Bull. Amer. Math. Soc. 71 (1965) 894--895.