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  • Articles  (66)
  • 2010-2014  (66)
  • 2012  (66)
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  • Articles  (66)
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  • 2010-2014  (66)
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  • 1
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    New preconditioners for systems of linear equations with Toeplitz structure (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-11-08
    Description:    In this paper, we consider applying the preconditioned conjugate gradient (PCG) method to solve system of linear equations T x = b where T is a block Toeplitz matrix with Toeplitz blocks (BTTB). We first consider Level -2 circulant preconditioners based on generalized Jackson kernels. Then, BTTB preconditioners based on a splitting of BTTB matrices are proposed. We show that the BTTB preconditioners based on splitting are special cases of embedding-based BTTB preconditioners, which are also good BTTB preconditioners. As an application, we apply the proposed preconditioners to solve BTTB least squares problems. Our preconditioners work for BTTB systems with nonnegative generating functions. The implementations of the construction of the preconditioners and the relevant matrix-vector multiplications are also presented. Finally, Numerical examples, including image restoration problems, are presented to demonstrate the efficiency of our proposed preconditioners. Content Type Journal Article Pages 1-25 DOI 10.1007/s10092-012-0074-0 Authors Yong-Jie Shi, Department of Mathematics, Shantou University, Shantou, 515063 Guangdong, China Xue-Bo Pi, Department of Mathematics, Shantou University, Shantou, 515063 Guangdong, China Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
    Print ISSN: 0008-0624
    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 2
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    On the numerical approximation of viscosity solutions for the differential-functional Cauchy problem (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-10-22
    Description:    We consider the Cauchy problem for first order differential-functional equations. We present finite difference schemes to approximate viscosity solutions of this problem. The functional dependence in the equation is of the Hale type. It contains, as a particular case, equation with a retarded and deviated argument, and differential-integral equation. Numerical examples to illustrate the theory are presented. Content Type Journal Article Pages 1-15 DOI 10.1007/s10092-012-0071-3 Authors Krzysztof A. Topolski, Institute of Mathematics, University of Gdaǹsk, Wit Stwosz 57, 80-952 Gdaǹsk, Poland Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Electronic ISSN: 1126-5434
    Topics: Mathematics
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  • 3
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    Accelerated iterative methods for finding solutions of nonlinear equations and their dynamical behavior (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-10-19
    Description:    In this paper, we present a family of optimal, in the sense of Kung–Traub’s conjecture, iterative methods for solving nonlinear equations with eighth-order convergence. Our methods are based on Chun’s fourth-order method. We use the Ostrowski’s efficiency index and several numerical tests in order to compare the new methods with other known eighth-order ones. We also extend this comparison to the dynamical study of the different methods. Content Type Journal Article Pages 1-14 DOI 10.1007/s10092-012-0073-1 Authors A. Cordero, Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain M. Fardi, Department of Mathematics, Islamic Azad University, Najafabad Branch, Najafabad, Iran M. Ghasemi, Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, Iran J. R. Torregrosa, Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Valencia, Spain Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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  • 4
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    A new family of Newton-type iterative methods with and without memory for solving nonlinear equations (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-10-01
    Description:    In this paper, we present a new family of two-step iterative methods for solving nonlinear equations. The order of convergence of the new family without memory is four requiring three functional evaluations, which implies that this family is optimal according to Kung and Traubs conjecture Kung and Traub (J Appl Comput Math 21:643–651, 1974 ). Further accelerations of convergence speed are obtained by varying a free parameter in per full iteration. This self-accelerating parameter is calculated by using information available from the current and previous iteration. The corresponding R-order of convergence is increased form 4 to \frac5+ Ö   17   2 » 4.5616, \frac5+ Ö   21   2 » 4.7913 and 5. The increase of convergence order is attained without any additional calculations so that the family of the methods with memory possesses a very high computational efficiency. Another advantage of the new methods is that they remove the severe condition f ¢ ( x ) in a neighborhood of the required root imposed on Newtons method. Numerical comparisons are made to show the performance of our methods, as shown in the illustration examples. Content Type Journal Article Pages 1-15 DOI 10.1007/s10092-012-0072-2 Authors Xiaofeng Wang, School of Mathematics and Physics, Bohai University, Jinzhou, 121013 Liaoning, China Tie Zhang, College of Sciences, Northeastern University, Shenyang, 110819 Liaoning, China Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
    Print ISSN: 0008-0624
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    Topics: Mathematics
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  • 5
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    The Pythagoras number of real sum of squares polynomials and sum of square magnitudes of polynomials (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-10-01
    Description:    In this paper, we conjecture a formula for the value of the Pythagoras number for real multivariate sum of squares polynomials as a function of the (total or coordinate) degree and the number of variables. The conjecture is based on the comparison between the number of parameters and the number of conditions for a corresponding low-rank representation. This is then numerically verified for a number of examples. Additionally, we discuss the Pythagoras number of (complex) multivariate Laurent polynomials that are sum of square magnitudes of polynomials on the n -torus. For both types of polynomials, we also propose an algorithm to numerically compute the Pythagoras number and give some numerical illustrations. Content Type Journal Article Pages 1-21 DOI 10.1007/s10092-012-0068-y Authors Thanh Hieu Le, Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Heverlee, Belgium Laurent Sorber, Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Heverlee, Belgium Marc Van Barel, Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001 Heverlee, Belgium Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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  • 6
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    A fast stationary iterative method for a partial integro-differential equation in pricing options (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-09-15
    Description:    A jump-diffusion model for the pricing of options leads to a partial integro-differential equation (PIDE). Discretizing the PIDE by certain method, we get a sequence of systems of linear equations, where the coefficient matrices are Toeplitz matrices. In this paper, we decompose the coefficient matrix as the sum of a tridiagonal matrix and a near low-rank matrix, and approximate the near low-rank matrix by low-rank matrices. Then we introduce a stationary iterative method for the approximate systems of linear equations. Comparison of the performance of our algorithm to that proposed in Pang et al. (Linear Algebra Appl. 434:2325–2342, 2011 ) is presented. Content Type Journal Article Pages 1-15 DOI 10.1007/s10092-012-0070-4 Authors Fu-Rong Lin, Department of Mathematics, Shantou University, Shantou, 515063 Guangdong, China Hai-Xia Yang, Department of Mathematics, Shantou University, Shantou, 515063 Guangdong, China Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
    Print ISSN: 0008-0624
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    Topics: Mathematics
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  • 7
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    Some results on the Drazin inverse of a modified matrix (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-09-09
    Description:    We give new conditions under which the Drazin inverse of a modified matrix A - CD D B can be expressed in terms of the Drazin inverse of A and its generalized Schur complement Z = D - BA D C , generalizing some recent results in the literature. Content Type Journal Article Pages 1-7 DOI 10.1007/s10092-012-0069-x Authors Dijana Mosić, Faculty of Sciences and Mathematics, University of Niš, P.O. Box 224, 18000 Niš, Serbia Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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  • 8
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    Convergence of parallel block SSOR multisplitting method for block H-matrix (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-08-21
    Description:    In this paper we investigate block SSOR multisplittings. When the coefficient matrix is a block H-matrix or a (generalized) block strictly diagonally dominant matrix, the convergence of the parallel block SSOR multisplitting method for solving nonsingular linear systems is proved. Two numerical examples are given to illustrate the theoretical results. Content Type Journal Article Pages 1-15 DOI 10.1007/s10092-012-0067-z Authors G. Cao, Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097 People’s Republic of China Y. Huang, Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097 People’s Republic of China Y. Song, Jiangsu Key Laboratory for NSLSCS, Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210097 People’s Republic of China Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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  • 9
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    A kinetic scheme for the one-dimensional open channel flow equations with applications on networks (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-08-21
    Description:    In this paper, a kinetic method to compute approximative solutions of the one-dimensional open channel flow equations with a varying cross-sectional area and a varying bottom profile is proposed. The scheme preserves the steady states at rest, keeps the water height non-negative and is able to handle dry channel beds. These three properties are essential indicators for the quality of a numerical scheme. The ability of the scheme to treat varying cross-sectional areas along the channel is an important advancement in comparison to previous papers. Further the same equations are considered on a network by coupling the equations at the nodes. The main difference to the majority of common numerical hydraulic models is the usage of the energy equality as coupling condition which seems to be more realistic than conditions based on the water height. Moreover, we set up a numerical method for computing subcritical flow on such networks. Several examples are treated to illustrate the results. Content Type Journal Article Pages 1-28 DOI 10.1007/s10092-012-0066-0 Authors Arne Roggensack, Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, 20146 Hamburg, Germany Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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  • 10
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    Numerical results for mimetic discretization of Reissner–Mindlin plate problems (2012)
    Springer
    In: CALCOLO
    Details
    Publication Date: 2012-08-21
    Description:    A low-order mimetic finite difference method for Reissner–Mindlin plate problems is considered. Together with the source problem, the free vibration and the buckling problems are investigated. Details about the scheme implementation are provided, and the numerical results on several different types of meshes are reported. Content Type Journal Article Pages 1-29 DOI 10.1007/s10092-012-0065-1 Authors Lourenço Beirão da Veiga, Dipartimento di Matematica “F. Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milan, Italy Carlo Lovadina, Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, 27100 Pavia, Italy David Mora, Departamento de Matemática, Universidad del Bío-Bío, Casilla 5-C, Concepción, Chile Journal Calcolo Online ISSN 1126-5434 Print ISSN 0008-0624
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    Topics: Mathematics
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