Displaying similar documents to “Some convergence acceleration processes for a class of vector sequences”

Solving conics over function fields

Mark van Hoeij, John Cremona (2006)

Journal de Théorie des Nombres de Bordeaux

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Let F be a field whose characteristic is not  2 and K = F ( t ) . We give a simple algorithm to find, given a , b , c K * , a nontrivial solution in  K (if it exists) to the equation a X 2 + b Y 2 + c Z 2 = 0 . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in F ; hence we obtain a recursive algorithm for solving diagonal conics over ( t 1 , , t n ) (using existing algorithms for such equations over  ) and over 𝔽 q ( t 1 , , t n ) .

Convergence of formal solutions of first order singular nonlinear partial differential equations in the complex domain

Masatake Miyake, Akira Shirai (2000)

Annales Polonici Mathematici

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We study the convergence or divergence of formal (power series) solutions of first order nonlinear partial differential equations    (SE) f(x,u,Dx u) = 0 with u(0)=0. Here the function f(x,u,ξ) is defined and holomorphic in a neighbourhood of a point ( 0 , 0 , ξ 0 ) x n × u × ξ n ( ξ 0 = D x u ( 0 ) ) and f ( 0 , 0 , ξ 0 ) = 0 . The equation (SE) is said to be singular if f(0,0,ξ) ≡ 0 ( ξ n ) . The criterion of convergence of a formal solution u ( x ) = | α | 1 u α x α of (SE) is given by a generalized form of the Poincaré condition which depends on each formal solution. In the case...

On the preconditioned biconjugate gradients for solving linear complex equations arising from finite elements

Michal Křížek, Jaroslav Mlýnek (1994)

Banach Center Publications

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The paper analyses the biconjugate gradient algorithm and its preconditioned version for solving large systems of linear algebraic equations with nonsingular sparse complex matrices. Special emphasis is laid on symmetric matrices arising from discretization of complex partial differential equations by the finite element method.

Existence of solutions of degenerated unilateral problems with L 1 data

Lahsen Aharouch, Youssef Akdim (2004)

Annales mathématiques Blaise Pascal

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In this paper, we shall be concerned with the existence result of the Degenerated unilateral problem associated to the equation of the type A u + g ( x , u , u ) = f - div F , where A is a Leray-Lions operator and g is a Carathéodory function having natural growth with respect to | u | and satisfying the sign condition. The second term is such that, f L 1 ( Ω ) and F Π i = 1 N L p ( Ω , w i 1 - p ) .

On Kelvin type transformation for Weinstein operator

Martina Šimůnková (2001)

Commentationes Mathematicae Universitatis Carolinae

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The note develops results from [5] where an invariance under the Möbius transform mapping the upper halfplane onto itself of the Weinstein operator W k : = Δ + k x n x n on n is proved. In this note there is shown that in the cases k 0 , k 2 no other transforms of this kind exist and for case k = 2 , all such transforms are described.