roots

Arguments

p

polynomial with real or complex coefficients or vector of the polynomial coefficients in decreasing degree order (Matlab compatibility).

Description

x=roots(p) returns in the complex vector x the roots of the polynomial p. For real polynomials of degree <=100 the fast RPOLY algorithm (based on Jenkins-Traub method) is used. In the other cases the roots are computed as the eigenvalues of the associated companion matrix. Use x=roots(p,'e') to force this algorithm in any cases.

Examples

p=poly([0,10,1+%i,1-%i],'x');
roots(p)
A=rand(3,3);roots(poly(A,'x'))    // Evals by characteristic polynomial
spec(A)

See Also

• poly — polynomial definition
• spec — eigenvalues of matrices and pencils
• companion — companion matrix

Authors

• Serge Steer (INRIA)

References

The RPOLY algorithm is described in "Algorithm 493: Zeros of a Real Polynomial", ACM TOMS Volume 1, Issue 2 (June 1975), pp. 178-189

Jenkins, M. A. and Traub, J. F. (1970), A Three-Stage Algorithm for Real Polynomials Using Quadratic Iteration, SIAM J. Numer. Anal., 7(1970), 545-566.

Jenkins, M. A. and Traub, J. F. (1970), Principles for Testing Polynomial Zerofinding Programs. ACM TOMS 1, 1 (March 1975), pp. 26-34

Used Functions

The rpoly.f source codes can be found in the directory SCI/modules/polynomials/src/fortran of a Scilab source distribution. In the case where the companion matrix is used, the eigenvalue computation is perfomed using DGEEV and ZGEEV LAPACK codes.