The computational complexity of continued fractions

The Knuth-Schönhage algorithm for expanding a quolynomial into a continued fraction is shown to be essentially optimal with respect to the number of multiplications/divisions used, uniformly in the inputs.

[1]  H. Wall,et al.  Analytic Theory of Continued Fractions , 2000 .

[2]  I. Shafarevich.  Basic algebraic geometry , 1974 .

[3]  Ephraim Feig.  Some results in algebraic complexity theory , 1980 .

[4]  George E. Collins,et al.  Subresultants and Reduced Polynomial Remainder Sequences , 1967, JACM.

[5]  Volker Strassen.  Computational Complexity over Finite Fields , 1976, SIAM J. Comput..

[6]  V. Strassen.  Die Berechnungskomplexität von elementarsymmetrischen Funktionen und von Interpolationskoeffizienten , 1973 .

[7]  T. Willmore.  Algebraic Geometry , 1973, Nature.

[8]  Pierre Samuel,et al.  Méthodes d'algèbre abstraite en géométrie algèbrique , 1956 .

[9]  Hlawka.  Einführung in die algebraische Geometrie , 1941 .

[10]  W. S. Brown,et al.  On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors , 1971, JACM.

[11]  Allan Borodin,et al.  The computational complexity of algebraic and numeric problems , 1975, Elsevier computer science library.

[12]  Alfred V. Aho,et al.  The Design and Analysis of Computer Algorithms , 1974 .

[13]  Claus-Peter Schnorr,et al.  An Extension of Strassen's Degree Bound , 1981, SIAM J. Comput..

[15]  Robert T. Moenck,et al.  Fast computation of GCDs , 1973, STOC.

[16]  V. Strassen.  Gaussian elimination is not optimal , 1969 .

[17]  Amiel Feinstein,et al.  Transmission of Information. , 1962 .

[18]  S. Lang.  Introduction to Algebraic Geometry , 1972 .

[19]  Joos Heintz,et al.  Lower Bounds for Polynomials with Algebraic Coefficients , 1980, Theor. Comput. Sci..

[20]  Arnold Schönhage.  An Elementary Proof for Strassen's Degree Bound , 1976, Theor. Comput. Sci..

[21]  H. T. Kung.  On computing reciprocals of power series , 1974 .

[22]  G. A. Barnard,et al.  Transmission of Information: A Statistical Theory of Communications. , 1961 .