Sequential and parallel complexity of approximate evaluation of polynomial zeros

[1]  D. H. Lehmer A Machine Method for Solving Polynomial Equations , 1961, JACM.

[2]  Donald Ervin Knuth,et al.  The Art of Computer Programming, Volume II: Seminumerical Algorithms , 1970 .

[3]  A. Householder The numerical treatment of a single nonlinear equation , 1970 .

[4]  M. A. Jenkins,et al.  A three-stage variable-shift iteration for polynomial zeros and its relation to generalized rayleigh iteration , 1970 .

[5]  P. Henrici,et al.  Circular arithmetic and the determination of polynomial zeros , 1971 .

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

[7]  M. Fischer,et al.  STRING-MATCHING AND OTHER PRODUCTS , 1974 .

[8]  Henry C. Thacher,et al.  Applied and Computational Complex Analysis. , 1988 .

[9]  Alfred V. Aho,et al.  Evaluating Polynomials at Fixed Sets of Points , 1975, SIAM J. Comput..

[10]  Paul Turán Power sum method and the approximative solution of algebraic equations , 1975 .

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

[12]  David Y. Y. Yun,et al.  Algebraic algorithms using p-adic constructions , 1976, SYMSAC '76.

[13]  E. W. Ng Symbolic and Algebraic Computation , 1979, Lecture Notes in Computer Science.

[14]  Maurice Mignotte,et al.  Some inequalities about univariate polynomials , 1981, SYMSAC '81.

[15]  S. Smale The fundamental theorem of algebra and complexity theory , 1981 .

[16]  Arnold Schönhage,et al.  The fundamental theorem of algebra in terms of computational complexity - preliminary report , 1982 .

[17]  J. Hopcroft,et al.  Fast parallel matrix and GCD computations , 1982, FOCS 1982.

[18]  Allan Borodin,et al.  Fast parallel matrix and GCD computations , 1982, 23rd Annual Symposium on Foundations of Computer Science (sfcs 1982).

[19]  Arnold Schönhage,et al.  Asymptotically Fast Algorithms for the Numerical Multiplication and Division of Polynomials with Complex Coeficients , 1982, EUROCAM.

[20]  Stephen A. Cook,et al.  The Classifikation of Problems which have Fast Parallel Algorithms , 1983, FCT.

[21]  Aivar A. Lorenc,et al.  Discrete Random Process Stabilization , 1983, Inf. Control..

[22]  Allan Borodin,et al.  Parallel Computation for Well-Endowed Rings and Space-Bounded Probabilistic Machines , 1984, Inf. Control..

[23]  Paul Turán,et al.  On a new method of analysis and its applications , 1984 .

[24]  Victor Y. Pan Fast and efficient algorithms for sequential and parallel evaluation of polynomial zeros and of matrix polynomials , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[25]  Leonidas J. Guibas,et al.  Parallel computational geometry , 1988, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[26]  Walter Keller-Gehrig,et al.  Fast Algorithms for the Characteristic Polynomial , 1985, Theor. Comput. Sci..

[27]  S. Smale,et al.  Computational complexity: on the geometry of polynomials and a theory of cost. I , 1985 .

[28]  Arnold Schönhage,et al.  Quasi-GCD computations , 1985, J. Complex..

[29]  S. Smale On the efficiency of algorithms of analysis , 1985 .

[30]  Michael Ian Shamos,et al.  Computational geometry: an introduction , 1985 .

[31]  Mikhail J. Atallah,et al.  Efficient Parallel Solutions to Some Geometric Problems , 1986, J. Parallel Distributed Comput..

[32]  Victor Y. Pan,et al.  Polynomial division and its computational complexity , 1986, J. Complex..

[33]  Ephraim Feig,et al.  A fast parallel algorithm for determining all roots of a polynomial with real roots , 1986, STOC '86.

[34]  Stephen Smale,et al.  Computational Complexity: On the Geometry of Polynomials and a Theory of Cost: II , 1986, SIAM J. Comput..

[35]  V. Pan Algebraic complexity of computing polynomial zeros , 1987 .

[36]  James Renegar,et al.  On the worst-case arithmetic complexity of approximating zeros of polynomials , 1987, J. Complex..

[37]  Victor Y. Pan,et al.  Complexity of Parallel Matrix Computations , 1987, Theor. Comput. Sci..

[38]  James Renegar On the Worst-Case Arithmetic Complexity of Approximating Zeros of Systems of Polynomials , 1989, SIAM J. Comput..