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Error estimates in L∞(0,T;L2(Ω)), L∞(0,T;L2(Ω)2), L∞(0,T;L∞(Ω)), L∞(0,T;L∞(Ω)2), Ω in $ℝ^{2}$ , are derived for a mixed finite element method for the initial-boundary value problem for integro-differential equation $u_{t} = div {a ▽ u + \int_{0}^{t} b_{1} ▽ u d τ + \int_{0}^{t} 𝐜 u d τ} + f$ based on the Raviart-Thomas space Vh x Wh ⊂ H(div;Ω) x L2(Ω). Optimal order estimates are obtained for the approximation of u,ut in L∞(0,T;L2(Ω)) and the associated velocity p in L∞(0,T;L2(Ω)2), divp in L∞(0,T;L2(Ω)). Quasi-optimal order estimates are obtained for the approximation...

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(2013)

Applications of Mathematics 2013

LMS-Newton adaptive filtering using FFT-based conjugate gradient iterations.

Ng, Michael K., Plemmons, Robert J. (1996)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Local a posteriori estimates for the Stokes problem.

Repin, S.I. (2004)

Zapiski Nauchnykh Seminarov POMI

Local analysis of a cubically convergent method for variational inclusions

Steeve Burnet, Alain Pietrus (2011)

Applicationes Mathematicae

This paper deals with variational inclusions of the form 0 ∈ φ(x) + F(x) where φ is a single-valued function admitting a second order Fréchet derivative and F is a set-valued map from $ℝ^{q}$ to the closed subsets of $ℝ^{q}$ . When a solution z̅ of the previous inclusion satisfies some semistability properties, we obtain local superquadratic or cubic convergent sequences.

Local and semilocal convergence theorems for Newton's method based on continuously Fréchet differentiable operators.

Argyros, Ioannis K. (2001)

Southwest Journal of Pure and Applied Mathematics [electronic only]

Local approximation estimators for algebraic multigrid.

Mandel, Jan (2003)

ETNA. Electronic Transactions on Numerical Analysis [electronic only]

Local behaviour of the derivative of a mid point cubic spline interpolator.

Dikshit, H.P., Rana, S.S. (1987)

International Journal of Mathematics and Mathematical Sciences

Local convergence analysis for a certain class of inexact methods.

Argyros, Ioannis K., Hilout, Saäid (2008)

The Journal of Nonlinear Sciences and its Applications

Local Convergence Analysis for Partitioned Quasi-Newton Updates.

A. Griewank, P.L. Toint (1982)

Numerische Mathematik

Local convergence analysis of a modified Newton-Jarratt's composition under weak conditions

Ioannis K. Argyros, Santhosh George (2019)

Commentationes Mathematicae Universitatis Carolinae

A. Cordero et. al (2010) considered a modified Newton-Jarratt's composition to solve nonlinear equations. In this study, using decomposition technique under weaker assumptions we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Local convergence analysis of inexact Newton-like methods.

Argyros, Ioannis K., Hilout, Said (2009)

The Journal of Nonlinear Sciences and its Applications

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Ljusternik acceleration and the extrapolated S.O.R. method

L∞(L2) and L∞(L∞) error estimates for mixed methods for integro-differential equations of parabolic type