jnaiamcont.org - Issues 3-4
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jnaiamcont.orgenSerendipity 1.5.4 - http://www.s9y.org/A Complete Orthogonal System of Spheroidal Monogenics
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<p><strong>J. Morais2<br />Freiberg University of Mining and Technology,<br />Institute of Applied Analysis, Prueferstr. 9, 09596 Freiberg, Germany<br />Received 26 November, 2010; accepted in revised form 28 July, 2011<br />Abstract: During the past few years considerable attention has been given to the role played<br />by monogenic functions in approximation theory. The main goal of the present paper is to<br />construct a complete orthogonal system of monogenic polynomials as solutions of the Riesz<br />system over prolate spheroids in R3 . This will be done in the spaces of square integrable<br />functions over R. As a first step towards is that the orthogonality of the polynomials in<br />question does not depend on the shape of the spheroids, but only on the location of the<br />foci of the ellipse generating the spheroid. Some important properties of the system are<br />briefly discussed.</strong></p>
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Mon, 18 Jun 2012 12:08:22 +0000http://jnaiam.org/index.php?/archives/108-guid.htmlOptimal Stability of Bivariate Tensor Product B-bases
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<p><strong>E. Mainar and Juan Manuel Pena<br />Departamento de Matematica Aplicada, Universidad de Zaragoza, Zaragoza, Spain<br />Received 15 December, 2009; accepted in revised form 18 October, 2011<br />Abstract: We analyze some properties of bivariate tensor product bases. In particular, we<br />obtain conditions so that a general bivariate tensor product basis is optimally stable for<br />evaluation. Finally, we apply our results to prove the optimal stability of tensor product<br />normalized B-bases.</strong></p>
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Mon, 18 Jun 2012 12:06:19 +0000http://jnaiam.org/index.php?/archives/107-guid.htmlA Uniformly Convergent Sequence of Spline Quadratures for Cauchy Principal Value Integrals
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<p><strong>C. Dagnino , V. Demichelis<br />Department of Mathematics, Faculty of Scienze Matematiche Fisiche e Naturali, University of Torino, 10100 Torino, Italy<br />Received 30 January, 2009; accepted in revised form 13 October, 2011<br />Abstract: We propose a new quadrature rule for Cauchy principal value integrals based<br />on quadratic spline quasi-interpolants which have an optimal approximation order and<br />satisfy boundary interpolation conditions. In virtue of these spline properties, we can<br />prove uniform convergence for sequences of such quadratures and provide uniform error<br />bounds. A computational scheme for the quadrature weights is given. Some numerical<br />results and comparisons with other spline methods are presented.</strong></p>
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Mon, 18 Jun 2012 12:05:05 +0000http://jnaiam.org/index.php?/archives/106-guid.htmlIterative Solution of Piecewise Linear Systems for the Numerical Solution of Obstacle Problems
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<p><strong>Luigi Brugnano and Alessandra Sestini<br />Dipartimento di Matematica “U. Dini” Viale Morgagni 67/A, 50134 Firenze, Italy<br />Dedicated to Prof. D. Trigiante on the occasion of his 65th birthday.<br />Received 16 December, 2009; accepted in revised form 24 September, 2011<br />Abstract: We investigate the use of piecewise linear systems, whose coefficient matrix is a<br />piecewise constant function of the solution itself. Such systems arise, for example, from<br />the numerical solution of linear complementarity problems and in the numerical solution<br />of free-surface problems. In particular, we here study their application to the numerical<br />solution of both the (linear) parabolic obstacle problem and the obstacle problem. We<br />propose a class of effective semi-iterative Newton-type methods to find the exact solution<br />of such piecewise linear systems. We prove that the semi-iterative Newton-type methods<br />have a global monotonic convergence property, i.e., the iterates converge monotonically<br />to the exact solution in a finite number of steps. Numerical examples are presented to<br />demonstrate the effectiveness of the proposed methods.</strong></p>
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Mon, 18 Jun 2012 12:00:03 +0000http://jnaiam.org/index.php?/archives/105-guid.html