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Convergence of Newtonlike Methods for Singular Operator Equations Using Outer Inverses
 Numer. Math
, 1993
"... this paper we consider Newtonlike methods (1:1) x k+1 = x k \Gamma A(x k ) ..."
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Cited by 14 (4 self)
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this paper we consider Newtonlike methods (1:1) x k+1 = x k \Gamma A(x k )
THE CONVERGENCE BALL OF NEWTONLIKE METHODS IN BANACH SPACE AND APPLICATIONS
"... Abstract. Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newtonlike methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton ..."
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Abstract. Under the hypothesis that the derivative satisfies some kind of weak Lipschitz condition, sharp estimates of the radii of convergence balls of Newtonlike methods for operator equations are given in Banach space. New results can be used to analyze the convergence of other developed Newton iterative methods. We consider the operator equation: 1.
On the factor refinement principle and its . . .
, 2011
"... The factor refinement principle turns a partial factorization of integers (or polynomials) into a more complete factorization represented by basis elements and exponents, with basis elements that are pairwise coprime. There are lots of applications of this refinement technique such as simplifying sy ..."
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The factor refinement principle turns a partial factorization of integers (or polynomials) into a more complete factorization represented by basis elements and exponents, with basis elements that are pairwise coprime. There are lots of applications of this refinement technique such as simplifying systems of polynomial inequations and, more generally, speeding up certain algebraic algorithms by eliminating redundant expressions that may occur during intermediate computations. Successive GCD computations and divisions are used to accomplish this task until all the basis elements are pairwise coprime. Moreover, squarefree factorization (which is the first step of many factorization algorithms) is used to remove the repeated patterns from each input element. Differentiation, division and GCD calculation operations are required to complete this preprocessing step. Both factor refinement and squarefree factorization often rely on plain (quadratic) algorithms for multiplication but can be substantially improved with asymptotically fast multiplication on