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rootbound

compute bound on complex roots of a polynomial

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

rootbound(p, x)

Parameters

p

-

polynomial in x with numeric coefficients

x

-

name

Description

• 

Returns a positive integer N such that &verbar;r&verbar;<N for all complex roots r of p.  In general, this bound is better than Cauchy's bound of

  

ceil1&plus;maxnormplcoeffp.

Examples

px&rarr;x410x2&plus;1&colon;

rootboundpx&comma;x

4

(1)

ceil1&plus;maxnormpxlcoeffpx

11

(2)

fsolvepx&equals;0&comma;x

3.146264370&comma;0.3178372452&comma;0.3178372452&comma;3.146264370

(3)

qx&rarr;x3.2x2.5x0.3x&plus;1.3x&plus;2.5x&plus;3.6&colon;

rootboundqx&comma;x

6

(4)

ceil1&plus;maxnormexpandqxlcoeffqx

78

(5)

References

  

Monagan, M.B. "A Heuristic Irreducibility Test for Univariate Polynomials." J. of Symbolic Comp. Vol. 13 No. 1. Academic Press, (1992): 47-57.

See Also

ceil

fsolve

lcoeff

maxnorm

 


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