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Higherorder deflation for polynomial systems with isolated singular solutions
 In IMA Volume 146: Algorithms in Algebraic Geometry
, 2008
"... Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolicnumeric deflation algorithm to restore the quadratic convergence of Newton’s method. Using firstorder derivatives of the polynomials in the system, our method creates an augmented ..."
Abstract

Cited by 14 (2 self)
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Given an approximation to a multiple isolated solution of a polynomial system of equations, we have provided a symbolicnumeric deflation algorithm to restore the quadratic convergence of Newton’s method. Using firstorder derivatives of the polynomials in the system, our method creates an augmented system of equations which has the multiple isolated solution of the original system as a regular root. In this paper we consider two approaches to computing the “multiplicity structure ” at a singular isolated solution. An idea coming from one of them gives rise to our new higherorder deflation method. Using higherorder partial derivatives of the original polynomials, the new algorithm reduces the multiplicity faster than our first method for systems which require several firstorder deflation steps. 2000 Mathematics Subject Classification. Primary 65H10. Secondary 14Q99, 68W30. Key words and phrases. Deflation, isolated singular solutions, Newton’s method, multiplicity, polynomial systems, reconditioning, symbolicnumeric computations.