10
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On the parallel arithmetic complexity of the root-finding problem

Pages 99-104 | Received 01 Sep 1986, Published online: 19 Mar 2007

References

  • Bitmead , R. R. and Anderson , B. D. O. 1980 . Assymptotically fast solution of Toeplitz and related systems of linear equations . Lin. Alg. Appl. , 34 : 103 – 116 .
  • Brent , R. and Luk , F. T. 1984 . A systolic array for linear-time solution of Toeplitz systems of equations . Journal of VLSI and Computer Systems , 1 ( 1 ) : 1 – 22 .
  • Brent R. Luk F. T. A systolic architecture for almost linear-time solution of the symmetric eigenvalue problem Technical Report TR-CS-82-10, Department of Computer Science Australian National University 1982
  • Datta , B. N. 1978 . Applications of Hankel matrices of Markov parameters to solutions of the Routh-Hurwitz and the Schur-Cohn problems . J. Math. Anal. Appl. , 68 ( 1 ) : 276 – 290 .
  • Datta , Karabi . 1985 . Parallel complexities and computations of Cholesky's decomposition and QR factorization . International Journal of Computer Mathematics , 18 ( 1 ) : 67 – 82 .
  • Gantmacher , F. R. 1959 . The Theory of Matrices Vol. II , Chelsea, New York
  • Gracar , J. and Sameh , A. 1981 . On certain parallel linear system solvers . SIAM J. Sci. Statist. Computing , 2 : 238 – 256 .
  • Kailath , T. , Vieira , A. and Morf , M. 1978 . Inverses of Toeplitz operators, innovations, and orthogonal polynomials . SIAM Review , 20 : 106 – 119 .
  • Krishnamurthy , E. V. and Venkateswaran , H. 1981 . A parallel algorithm for complex zeros of a polynomial . BIT , 21 : 104 – 111 .
  • Kung , S. Y. and Hu , Y. H. 1983 . A highly concurrent algorithm and pipelined architecture for solving Toeplitz systems . IEEE Trans. on Acoustics, Speech and Signal Processing , 31 ( 1 ) : 66 – 76 . ASSP
  • Phillips , James L. 1971 . The triangular decomposition of Hankel matrices . Mathematics of Computation , 25 ( 1 ) : 599 – 602 .
  • Sameh , A. H. and Kuck , D. J. 1977 . A parallel QR algorithm for symmetric tridiagonal matrices . IEEE Trans. Computers , C-26 ( 1 ) : 147 – 153 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.