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Evaluating numerical ODE/DAE methods, algorithms and software

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2006年第2期185卷 244-260页

作者： Söderlind, G Wang, L Lund Univ Ctr Math Sci SE-22100 Lund Sweden

Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one methods better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol;without it conclusions are questionable, invalid or even false. We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to D-ASPK and R(ADAU)5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems. (c) 2005 Published by Elsevier B.V.

关键词： software testing test protocols computational stability ODE software DAE software work/precision adaptive time-stepping mathematical software algorithm analysis

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On the Effectiveness of Genetic Operations in Symbolic Regression 1

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15th International Conference on Computer Aided Systems Theory

作者： Burlacu, Bogdan Affenzeller, Michael Kommenda, Michael Univ Appl Sci Upper Austria Heurist & Evolutionary Algorithms Lab Sch Informat Commun & Media Softwarepk 11 A-4232 Hagenberg Austria Johannes Kepler Univ Linz Inst Formal Models & Verificat A-4040 Linz Austria

ISBN: (数字)9783319273402

ISBN: (纸本)9783319273402;9783319273396

This paper describes a methodology for analyzing the evolutionary dynamics of genetic programming (GP) using genealogical information, diversity measures and information about the fitness variation from parent to offspring. We introduce a new subtree tracing approach for identifying the origins of genes in the structure of individuals, and we show that only a small fraction of ancestor individuals are responsible for the evolvement of the best solutions in the population.

关键词： Genetic programming Evolutionary dynamics algorithm analysis Symbolic regression

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Faster exponential time algorithms for the shortest vector problem

Faster exponential time algorithms for the shortest vector p...

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21st Annual ACM/SIAM Symposium on Discrete algorithms

作者： Micciancio, Daniele Voulgaris, Panagiotis Univ Calif San Diego La Jolla CA 92093 USA

ISBN: (纸本)9780898717013

We present new faster algorithms for the exact solution of the shortest;vector problem in arbitrary lattices Our main result shows that the shortest vector in any n-dimensional lattice can be found in time 2(3) (199n) (and space 2(1) (325n)), or in Space 2(1) (095n) (and still tune 2(O(n))). Tins improves the best previously known algorithm by Ajtai, Kumar and Sivakumar [Proceedings of STOC 2001] which was shown by Nguyen and Vidick [J Math Crypto. 2(2) 181-207] to inn in time 2(5) (9n) and space 2(2) (95n) We also present a practical variant of our algorithm which provably uses an amount of space proportional to tau(n), the "kissing" constant in dimension n. No upper bound on the running tune of our second algorithm is currently known, but experimentally the algorithm seems 1,0 perforin fairly well in practice with running Lime 2(0) (52n) and space complexity 2(0) (2n)

关键词： algorithm analysis Cryptography Shortest Vector Problem Sieving algorithms Software implementations

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High-Speed Packet Classification: A Case for Approximate Sorting

High-Speed Packet Classification: A Case for Approximate Sor...

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IEEE Global Communications Conference (GLOBECOM)

作者： Narasimhan, Aditya Radhakrishnan, Sridhar Atiquzzaman, Mohammad Subramanian, C. R. Univ Oklahoma Sch Comp Sci Norman OK 73019 USA HBNI Inst Math Sci Chennai 600113 Tamil Nadu India

ISBN: (纸本)9781665435406

Buffer capacities at routers are ever-increasing to accommodate the extreme-scale increase in the volume of incoming traffic. Sophisticated packet classification is being adopted to address challenges in meeting application demands. With the number of rules for classification and packets arriving at routers per second reaching 100's of thousands to millions, special hardware is also being built for packet classification to increase throughput at routers. Sorting packets (based on various conditions) in the buffers offers a significant advantage for the packet classification process. The sorting step is a time-consuming step given the large volume of packets in the incoming buffers. We propose a technique to approximately sort the packets by capping the maximum number of comparisons that can be made. We show that the performance of well-known decision tree-based packet classification methods such as HyperCuts, EffiCuts, and SmartSplits can be improved by more than 32% with approximate sorting for when the number of packets is less than 10K at any given time. If the number of packets in the arriving buffer is greater than 10K, we can divide them into smaller portions to achieve similar gains.

关键词： Buffer Management Packet Classification Approximate Sorting algorithm analysis

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Robust algorithm for Signal Digital Detection on the Background of Non-Gaussian Passive Interferences

Robust Algorithm for Signal Digital Detection on the Backgro...

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Workshop on Microwave Theory and Techniques in Wireless Communications (MTTW)

作者： Yanovsky, Felix Prokopenko, Igor Rhee, Huinam Pitertsev, Alexander Dmytruk, Anastasiia Natl Aviat Univ Dept Elect Robot Monitoring & IoT Technol ERMIT Kiev Ukraine Delft Univ Technol Dept Geosci & Remote Sensing Atmospher Remote Sensing Delft Netherlands Natl Aviat Univ Dept Aeronav Radio Elect & Telecomun Kiev Ukraine Sunchon Natl Univ Dept Aerosp Engn Aerosp Res Ctr Sunchon South Korea Natl Aviat Univ Dept Elect Robot Monitoring & IoT Technol Kiev Ukraine

ISBN: (数字)9781665464390

ISBN: (纸本)9781665464390

This paper proposes generalized mathematical model of different passive interferences and develops an effective algorithm of digital signal processing for detection on the background of them. Models of interferences as random process of K-distribution is used with parametrization for the unwanted reflections from atmosphere, land, and sea. Robust algorithm for signal detection on the background of such interferences, in particular in case of non-gaussian distribution, is developed. Its effectiveness is researched and confirmed.

关键词： digital signal processing radar detection clutter algorithm design algorithm analysis ranking

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Optimal Parallel Sorting with Comparison Errors 23

Optimal Parallel Sorting with Comparison Errors

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35th ACM Symposium on Parallelism in algorithms and Architectures (SPAA)

作者： Goodrich, Michael T. Jacob, Riko Univ Calif Irvine Irvine CA 92697 USA IT Univ Copenhagen Copenhagen Denmark

ISBN: (纸本)9781450395458

We present comparison-based parallel algorithms for sorting n comparable items subject to comparison errors. We consider errors to occur according to a well-studied framework, where the comparison of two elements returns the wrong answer with a fixed probability. In the persistent model, the result of the comparison of two given elements, x and y, always has the same result, and is independent of all other pairs of elements. In the non-persistent model, the result of the comparison of each pair of elements, x and y, is independent of all prior comparisons, including for x and y. It is not possible to always correctly sort a given input set in the persistent model, so we study algorithms that achieve a small maximum dislocation and small total dislocation of the elements in the output permutation. In this paper, we provide parallel algorithms for sorting with comparison errors in the persistent and non-persistent models. Our algorithms are asymptotically optimal in terms of their span, work, and, in the case of persistent errors, maximum and total dislocation. The main results are algorithms for the binary-forking parallel model with atomics, but we also provide algorithms for the CREW PRAM model. Our algorithms include a number of novel techniques and analysis tools, including a PRAM-to-binary-forking-model simulation result, and are the first optimal parallel algorithms for the persistent model and the non-persistent model in the binary-forking parallel model with atomics. In particular, our algorithms haveO(log n) span, O(n log n) work, and, in the case of the persistent model, O(log n) maximum dislocation and O(n) total dislocation, with high probability. We achieve similar results for the CREW PRAM model, which are the first optimal methods for the persistent model and the first optimal results for the non-persistent model with reasonable constant factors in the performance bounds.

关键词： sorting noisy searching algorithm analysis randomized algorithms

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Quad tree based algorithm for building of network model from road layers of vector maps 3

Quad tree based algorithm for building of network model from...

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3rd IEEE International Conference on Recent Advances in Information Technology (RAIT)

作者： Alampatta, Shibumon Rajesh, M. A. Panigrahi, Narayan Def Res & Dev Org Ctr Artificial Intelligence & Robot Bangalore Karnataka India

ISBN: (纸本)9781479985791

Modeling of a graph corresponding to transport network from vector layers of a digital map is essential to carry out any sort of network analysis operations. In vector maps, feature objects in road layers are generally modeled as simple features which do not capture the connectivity information. This paper proposes a method for building a network/graph model from such road layers of a vector map. In this work a quad tree based algorithm for building of network is proposed, which offers a linear time complexity whereas the trivial method is quadratic in order of complexity.

关键词： network building road layer transportation network graph quad tree algorithm analysis geographical information system vector maps

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An Improved Complex Network Community Detection algorithm Based on K-Means

An Improved Complex Network Community Detection Algorithm Ba...

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Conference on the Future Computer and Control Systems

作者： Wang, Yuqin Jilin Business & Technol Coll Dept Informat Engn Changchun 130062 Peoples R China

ISBN: (纸本)9783642293894

In order to find community structure that exists in complex network structure, this paper introduced K-means approach to the complex network community structure of the research. This paper studies the complex network of community structure detection algorithm, through the existing algorithm learn and study, proposed an improved algorithm based on K-means. Not know the premise of community structure for the complex networks division, the algorithm is simple and easy to understand, and the algorithm was used in karate network, through experimental verification, experimental results show that the algorithm is effective.

关键词： complex networks community structure k-means detection algorithm algorithm analysis

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Impact of algorithm Complexity on Energy Utilization of Wireless Sensor Nodes 5

Impact of Algorithm Complexity on Energy Utilization of Wire...

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International Conference on Advances in Computing, Communications and Informatics (ICACCI)

作者： Lekshmy, V. M. Rekha, P. Ramesh, Maneesha Vinodhini Amrita Univ Amrita Sch Engn Amrita Ctr Wireless Networks & Applicat Amritapuri Campus Kollam Kerala India

ISBN: (纸本)9781509020287

Nowadays wireless sensor networks are implemented in a variety of fields to obtain real-time measurements. These networks are comprised of small, low cost devices called wireless sensor nodes (WSN). There are different types of wireless sensor nodes available in the market. Based on the requirements, wireless sensor nodes can be selected for each application. Power consumption is a major aspect in developing wireless sensor applications. In this paper, analysis of power consumption in different sensor nodes is conducted based on algorithms with different complexities. The experimental analysis results show that at a particular input current limit, Waspmote consumes 15% less power than MICAz mote in the case of O (1), 11.04% less in the case of O (n), 7.6% less in the case of O (n2), 3.9% less in case of O (log n) and 18.06% less in case of O (m+n) complex algorithms.

关键词： mote algorithm analysis complexity power consumption

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Adaptive time-stepping and computational stability

Adaptive time-stepping and computational stability

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International Workshop on the Technological Aspects of Mathematics

作者： Söderlind, G Wang, L Lund Univ Ctr Math Sci SE-22100 Lund Sweden

We investigate the effects of adaptive time-stepping and other algorithmic strategies on the computational stability of ODE codes. We show that carefully designed adaptive algorithms have a most significant impact on computational stability and reliability. A series of computational experiments with the standard implementation of D-ASSL and a modified version, including stepsize control based on digital filters, is used to demonstrate that relatively small algorithmic changes are able to extract a vastly better computational stability at no extra expense. The inherent performance and stability of DASSL are therefore much greater than the standard implementation seems to suggest. (c) 2005 Elsevier B.V. All rights reserved.

关键词： computational stability stepsize control adaptive time-stepping PI control digital filters DASSL mathematical software algorithm analysis

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