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Approximation Theory and the Design of Fast Algorithms [article]

Sushant Sachdeva, Nisheeth Vishnoi
2013 arXiv   pre-print
We then present a selection of results demonstrating how such approximations can be used to speed up primitives crucial for the design of fast algorithms for problems such as simulating random walks, graph  ...  We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^-x, 1/x, and x^k.  ...  We would like to thank Elisa Celis and Oded Regev for useful discussions. We would also like to thank László Babai for helpful comments.  ... 
arXiv:1309.4882v1 fatcat:al7qezjt6jbrfe3pk6ar2xffz4

Fast Approximate Graph Partitioning Algorithms

Guy Even, Joseph (Seffi) Naor, Satish Rao, Baruch Schieber
1999 SIAM journal on computing (Print)  
During last decade, several approximation algorithms have been designed for computing tree-decompositions of graphs Even+99, Bouchitté+01, Feige+05] .  ...  This will be useful to validate the exact and heuristic algorithms.  ...  This will be useful to validate the exact and heuristic algorithms. Required background: graph theory, algorithmic, optimization, computational complexity, JAVA and/or PYTHON  ... 
doi:10.1137/s0097539796308217 fatcat:vydnmxdch5hbbaaxefmytnem7q

Page 3417 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
This recursive algorithm takes its inspi- ration from the well-known fast-multipole method. At the end of this paper we give some physical applications of this algorithm.”  ...  Summary: “A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function LP f(teimdt, -1<x<y<1, w £0, where the Chebyshev se-  ... 

Page 9552 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
The two algorithms are called RLS-TD(A) and Fast-AHC (Fast Adaptive Heuristic Critic), respectively.  ...  We are interested in the rate of this convergence. This approximation problem arose from the study of learning theory, where B is the L> space and # is a reproducing kernel Hilbert space.  ... 

Page 6566 of Mathematical Reviews Vol. , Issue 99i [page]

1999 Mathematical Reviews  
Computer simulation results have shown that the algorithm is stable and converges fast often with a rate which is comparable to that of the known CG and RLS algorithm.  ...  of images, for addressing issues associated with the development of algorithms based on these optimality criteria, and for quantifying the quality of the approximations.  ... 

Solving the optimal PWM problem for single-phase inverters

D. Czarkowski, D.V. Chudnovsky, I.W. Selesnick
2002 IEEE Transactions on Circuits and Systems I Fundamental Theory and Applications  
The reformulation draws upon the Newton identities, Padé approximation theory, and properties of symmetric functions.  ...  Specifically, it is shown that the nonlinear design equations given by the standard mathematical formulation of the problem can be reformulated, and that the sought solution can be found by computing the  ...  ACKNOWLEDGMENT The authors wish to thank H. Huang for helpful comments on the manuscript.  ... 
doi:10.1109/81.995661 fatcat:zttjk6uawnax3imgmvzgh77d5u

Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange

Jonathan E. Moussa
2014 Journal of Chemical Physics  
The algorithm comparably reduces the scaling of second-order Møller-Plesset (MP2) perturbation theory with smaller cost prefactors than RPA+SOSEX.  ...  The random-phase approximation with second-order screened exchange (RPA+SOSEX) is a model of electron correlation energy with two caveats: its accuracy depends on an arbitrary choice of mean field, and  ...  FAST ALGORITHM DESIGN Here we design fast and conventional algorithms for MP2 and RPA+SOSEX calculations. In each of these four designs, we begin by identifying the tensor equations to be evaluated.  ... 
doi:10.1063/1.4855255 pmid:24410221 fatcat:w3ujec3efvbopgr53vbuiifz4m

Structural parallel algorithmics [chapter]

Uzi Vishkin
1991 Lecture Notes in Computer Science  
Consequences of the above discussion are: (1) the evolving theory of very fast parallel algorithms cannot benefit from the theory of notas-fast parallel algorithms; and (2) any result that approaches the  ...  The benefit from the PRAM model is not only in the extensive list of efficient and fast parallel algorithms that have been designed.  ... 
doi:10.1007/3-540-54233-7_148 fatcat:7itpvjsg7ngmbdh4aj6xpxe2he

Model-Free Composite Control of Flexible Manipulators Based on Adaptive Dynamic Programming

Chunyu Yang, Yiming Xu, Linna Zhou, Yongzheng Sun
2018 Complexity  
In the fast timescale, the vibration is reconstructed based on the measurements of vibration and its estimate in the slow timescale, by which the fast controller is designed using ADP.  ...  Stability of the closed-loop system is proved by SP theory. Finally, simulations are given to show the feasibility and effectiveness of the proposed methods.  ...  Acknowledgments This work was supported by the Fundamental Research Funds for the Central Universities under Grant 2017XKQY 055.  ... 
doi:10.1155/2018/9720309 fatcat:csgrrsoslbaibmkuvpcfcxwnu4

Page 3228 of Mathematical Reviews Vol. , Issue 82g [page]

1982 Mathematical Reviews  
LivSic, An introductory lecture to the theory of open systems (pp. 105-109); Malcolm MacLeod, The design of digital filters using cycled coefficients (pp. 131-136); Rolf Unbehauen, On the design of digital  ...  approximation algorithms and Levinson/Schur recursive methods (pp. 517-523); D.  ... 

Model Reduction Design of Multivariable Aircraft System Using Fast Haar Transform Algorithm

Joon-Hoon Park, Ryum-Duk Oh
2017 International Journal of Control and Automation  
The model reduction method adopted in this paper is that of system approximation algorithm using the fast Haar transform. This approach provides more convenient and efficient results.  ...  Therefore the analysis and design effort can be reduced. The Haar function set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions.  ...  We can also approximate high-order transfer function as low-order transfer function Ĝij(s) based on the similarity condition and the fast Haar transforming algorithm [11] .  ... 
doi:10.14257/ijca.2017.10.12.01 fatcat:pqqz2l5h5vdrbkwj45yewuu6ue

New Results on CGR/CUR Approximation of a Matrix [article]

Victor Y. Pan
2016 arXiv   pre-print
We conclude the paper with novel extensions of our acceleration to the Fast Multipole Method and the Conjugate Gradient Algorithms. (This report is an outline of our paper in arXiv:1611.01391.)  ...  Our study provides new insights and enable design of faster algorithms for low-rank approximation by means of sampling and oversampling, for Gaussian elimination with no pivoting and block Gaussian elimination  ...  Besides providing a new insight into the subject, this motivates the design of more efficient algorithms and shows specific direction to this goal.  ... 
arXiv:1607.04825v2 fatcat:27sidapntbhclmmstpjofiavnm

Introduction [chapter]

B. Preneel
1995 Lecture Notes in Computer Science  
In parallel, the generalization of specific attacks leads to the development of a theory which supports both the design and analysis activity.  ...  The goal of this series of workshops is to advance our understanding of software algorithms for two cryptographic primitives which require very high speeds, namely encryption algorithms and hash functions  ...  I also would like to thank the organizing committee: for the hard work and for the fine collaboration, and Lars R. Knudsen and Kaisa Nyberg for helping with the review of a paper.  ... 
doi:10.1007/3-540-60590-8_1 fatcat:u5nakd5chnfc3ifhut5rc4xqba

Page 2360 of Mathematical Reviews Vol. , Issue 90D [page]

1990 Mathematical Reviews  
(Japanese) [Mathematical theory of the boundary element method and related topics.  ...  Benson and Paul O. Frederickson, Fast parallel algorithms for the Moore- Penrose pseudo-inverse (pp. 597-604); P. J.  ... 

A continuum limit for non-dominated sorting

Jeff Calder, Selim Esedoglu, Alfred O. Hero
2014 2014 Information Theory and Applications Workshop (ITA)  
We show how this PDE can be used to design a fast, potentially sublinear, approximate non-dominated sorting algorithm, and we show the results of applying the algorithm to real data from an anomaly detection  ...  Non-dominated sorting is an important combinatorial problem in multi-objective optimization, which is ubiquitous in many fields of science and engineering.  ...  ACKNOWLEDGMENT The research described in this paper was partially supported by ARO grant W911NF-09-1-0310 and NSF grants CCF-1217880 and DMS-0914567.  ... 
doi:10.1109/ita.2014.6804207 dblp:conf/ita/CalderEH14 fatcat:rdjv4xfzlrepvfr7lgqioxetuu
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