C209: Zeros of a Complex Polynomial

Author(s): T. Pomentale Library: MATHLIB
Submitter: K.S. Kölbig Submitted: 07.06.1992
Language: Fortran Revised:

Subroutine subprograms CPOLYZ and WPOLYZ compute the zeros of the polynominal

displaymath91

of degree n with complex coefficients tex2html_wrap_inline95 and tex2html_wrap_inline97 .

On computers other than CDC or Cray, only the double-precision version WPOLYZ is available. On CDC and Cray computers, only the single-precision version CPOLYZ is available.

Structure:

SUBROUTINE subprograms
User Entry Names: CPOLYZ, WPOLYZ
Files Referenced: Unit 6
External References: MTLMTR, ABEND

Usage:

For tex2html_wrap_inline99 (type COMPLEX), tex2html_wrap_inline101 (type COMPLEX*16),

    CALL tPOLYZ(C,N,MAXIT,Z,R)
C
(type according to t) One-dimensional array of dimension (0:d), where tex2html_wrap_inline103 , containing the coefficients tex2html_wrap_inline105 .
N
(INTEGER) The degree n.
MAXIT
(INTEGER) The maximum number of iterations permitted.
Z
(type according to t) One-dimensional array of length tex2html_wrap_inline109 . On entry, tex2html_wrap_inline111 must contain starting approximations for the zeros tex2html_wrap_inline113 . If no starting approximations are available, the tex2html_wrap_inline115 should be set to zero. On exit, tex2html_wrap_inline117 contains an approximation to the zero tex2html_wrap_inline119 .
R
(REAL for tex2html_wrap_inline121 , DOUBLE PRECISION for tex2html_wrap_inline123 ) One-dimensional array of dimension tex2html_wrap_inline125 . On exit, tex2html_wrap_inline127 contain an estimated radius tex2html_wrap_inline129 of a circle centered at tex2html_wrap_inline131 within which the true zero tex2html_wrap_inline133 is expected to lie.

Notes:

Note that, because of accumulation of rounding errors, unreliable results can be obtained for large n even for well-conditioned polynomials.

Error handling:

Error C209.1: tex2html_wrap_inline137 .
Error C209.2: The number of iterations exceeds MAXIT.
Error C209.3: An estimated radius tex2html_wrap_inline139 cannot be computed for a certain value of i.
In all cases, a message is written on Unit 6, unless subroutine MTLSET (N002) has been called.

References:

  1. T. Pomentale, Homotopy iterative methods for polynomial equations, J. Inst. Maths. Applics. 13 (1974) 201-213.
tex2html_wrap_inline143

Michel Goossens Tue Jun 4 20:51:55 METDST 1996