The method of seconds with extrapolation for accurate calculation of manifold roots

The problem is investigated to calculate accurately many fold roots of a nonlinear algebraic equation. The algorithm is constructed for founding of multiplicity of roots in frame of the method of seconds. The recurrent extrapolation is proposed to improve an accuracy in 100–1000 times. The FORTRAN code SECWEX is written. It gives the value of a root an asymptotically exact which is an estimation of it’s error and an estimation of it’s multiplicity. The code is robust when multiplicity is up to 10.