Special Issue "Algorithms for Applied Mathematics"

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A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 April 2010)

Special Issue Editor

Guest Editor
Prof. Dr. Doron Levy

Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA
Website | E-Mail
Phone: +1^301 405 5140

Keywords

  • discrete models
  • stochastic equations
  • ordinary differential equations
  • time-delayed equations
  • partial differential equations
  • finite-volume, finite difference, finite elements methods
  • particle methods
  • spectral methods
  • linear and nonlinear optimization
  • linear algebra

Published Papers (6 papers)

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Research

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Open AccessArticle Univariate Cubic L1 Interpolating Splines: Spline Functional, Window Size and Analysis-based Algorithm
Algorithms 2010, 3(3), 311-328; doi:10.3390/a3030311
Received: 11 July 2010 / Accepted: 10 August 2010 / Published: 20 August 2010
Cited by 7 | PDF Full-text (327 KB) | HTML Full-text | XML Full-text
Abstract
We compare univariate L1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that
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We compare univariate L1 interpolating splines calculated on 5-point windows, on 7-point windows and on global data sets using four different spline functionals, namely, ones based on the second derivative, the first derivative, the function value and the antiderivative. Computational results indicate that second-derivative-based 5-point-window L1 splines preserve shape as well as or better than the other types of L1 splines. To calculate second-derivative-based 5-point-window L1 splines, we introduce an analysis-based, parallelizable algorithm. This algorithm is orders of magnitude faster than the previously widely used primal affine algorithm. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
Open AccessArticle Univariate Cubic L1 Interpolating Splines: Analytical Results for Linearity, Convexity and Oscillation on 5-PointWindows
Algorithms 2010, 3(3), 276-293; doi:10.3390/a3030276
Received: 9 June 2010 / Revised: 11 July 2010 / Accepted: 20 July 2010 / Published: 30 July 2010
Cited by 5 | PDF Full-text (150 KB) | HTML Full-text | XML Full-text
Abstract
We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity
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We analytically investigate univariate C1 continuous cubic L1 interpolating splines calculated by minimizing an L1 spline functional based on the second derivative on 5-point windows. Specifically, we link geometric properties of the data points in the windows with linearity, convexity and oscillation properties of the resulting L1 spline. These analytical results provide the basis for a computationally efficient algorithm for calculation of L1 splines on 5-point windows. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
Open AccessArticle Computation of the Metric Average of 2D Sets with Piecewise Linear Boundaries
Algorithms 2010, 3(3), 265-275; doi:10.3390/a3030265
Received: 5 May 2010 / Revised: 8 July 2010 / Accepted: 22 July 2010 / Published: 26 July 2010
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Abstract
The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with piecewise
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The metric average is a binary operation between sets in Rn which is used in the approximation of set-valued functions. We introduce an algorithm that applies tools of computational geometry to the computation of the metric average of 2D sets with piecewise linear boundaries. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
Open AccessArticle Segment LLL Reduction of Lattice Bases Using Modular Arithmetic
Algorithms 2010, 3(3), 224-243; doi:10.3390/a3030224
Received: 28 May 2010 / Accepted: 29 June 2010 / Published: 12 July 2010
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Abstract
The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction
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The algorithm of Lenstra, Lenstra, and Lovász (LLL) transforms a given integer lattice basis into a reduced basis. Storjohann improved the worst case complexity of LLL algorithms by a factor of O(n) using modular arithmetic. Koy and Schnorr developed a segment-LLL basis reduction algorithm that generates lattice basis satisfying a weaker condition than the LLL reduced basis with O(n) improvement than the LLL algorithm. In this paper we combine Storjohann’s modular arithmetic approach with the segment-LLL approach to further improve the worst case complexity of the segment-LLL algorithms by a factor of n0.5. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
Open AccessArticle Algorithmic Solution of Stochastic Differential Equations
Algorithms 2010, 3(3), 216-223; doi:10.3390/a3030216
Received: 17 May 2010 / Revised: 15 June 2010 / Accepted: 29 June 2010 / Published: 1 July 2010
PDF Full-text (207 KB) | HTML Full-text | XML Full-text
Abstract
This brief note presents an algorithm to solve ordinary stochastic differential equations (SDEs). The algorithm is based on the joint solution of a system of two partial differential equations and provides strong solutions for finite-dimensional systems of SDEs driven by standard Wiener processes
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This brief note presents an algorithm to solve ordinary stochastic differential equations (SDEs). The algorithm is based on the joint solution of a system of two partial differential equations and provides strong solutions for finite-dimensional systems of SDEs driven by standard Wiener processes and with adapted initial data. Several examples illustrate its use. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)

Review

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Open AccessReview An Introduction to Clique Minimal Separator Decomposition
Algorithms 2010, 3(2), 197-215; doi:10.3390/a3020197
Received: 7 April 2010 / Accepted: 28 April 2010 / Published: 14 May 2010
Cited by 17 | PDF Full-text (164 KB) | HTML Full-text | XML Full-text
Abstract
This paper is a review which presents and explains the decomposition of graphs by clique minimal separators. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as
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This paper is a review which presents and explains the decomposition of graphs by clique minimal separators. The pace is leisurely, we give many examples and figures. Easy algorithms are provided to implement this decomposition. The historical and theoretical background is given, as well as sketches of proofs of the structural results involved. Full article
(This article belongs to the Special Issue Algorithms for Applied Mathematics)
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