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Low complexity algorithms for linear recurrences

A. Bostan, F. Chyzak, B. Salvy, T. Cluzeau
2006 Proceedings of the 2006 international symposium on Symbolic and algebraic computation - ISSAC '06  
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation  ...  The algorithms for these tasks all involve as an intermediate quantity an integer N (dispersion or root of an indicial polynomial) that is potentially exponential in the bit size of their input.  ...  Thus, it makes an important contribution to the complexity of these algorithms. Once this form is computed, these algorithms search for polynomial solutions of an associated linear recurrence.  ... 
doi:10.1145/1145768.1145781 dblp:conf/issac/BostanCSC06 fatcat:2eh2lnt7rbcsvjsrpfpwbuysci

Page 5221 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
The Berlekamp algorithm was developed as an algorithm for solving a Hankel system of linear equations over a finite field.  ...  The computational complexity is the same as the complexity of the original Berlekamp-Massey algorithm. Boris D. Kudryashov (St.  ... 

Deep clustering of longitudinal data [article]

Louis Falissard, Guy Fagherazzi, Newton Howard, Bruno Falissard
2018 arXiv   pre-print
These methods provide a framework to model complex, non-linear interactions in large datasets, and are naturally suited to the analysis of hierarchical data such as, for instance, longitudinal data with  ...  the use of recurrent neural networks.  ...  linear models for repeated measures.  ... 
arXiv:1802.03212v1 fatcat:t4ceogbunvhvhjlwye3lpjbxqu

Page 1729 of Mathematical Reviews Vol. , Issue 95c [page]

1995 Mathematical Reviews  
The main result of the paper is an algorithm for computing an approximating matrix with a model of (much) lower complexity than the original—as low as possible for a given tolerance on the approximation  ...  ); Dewilde, Patrick (NL-DELF-E; Delft) On low-complexity approximation of matrices.  ... 

Nonlinear predictive control based on neural multi-models

Maciej Ławryńczuk, Piotr Tatjewski
2010 International Journal of Applied Mathematics and Computer Science  
This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated.  ...  predictive control based on neural multi-models This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm  ...  Acknowledgment The work presented in this paper was supported by the Polish national budget funds for science for the years 2009-2011 in the framework of a research project.  ... 
doi:10.2478/v10006-010-0001-y fatcat:cphqe7sxofdzbpam3iejj5nutq

On the numerical evaluation of linear recurrences

R. Barrio, B. Melendo, S. Serrano
2003 Journal of Computational and Applied Mathematics  
We present some remarks on the numerical evaluation of recurrence relations.  ...  limit case of Jacobi-Sobolev polynomials, random recurrences and perturbed Gegenbauer polynomials.  ...  of algorithms with low computational complexity [10] .  ... 
doi:10.1016/s0377-0427(02)00565-4 fatcat:corz322or5ehdaqpuodfje7hse

Page 4072 of Mathematical Reviews Vol. , Issue 93g [page]

1993 Mathematical Reviews  
The authors consider a so-called “low-complexity algorithmfor linear programming problems in standard form with n variables. This algorithm requires only O(,/nt) iterations to attain precision t.  ...  The authors show that, after an initial centering phase, the low-complexity algorithm is a predictor-corrector path-following method.  ... 

A Two-pronged Progress in Structured Dense Matrix Vector Multiplication [chapter]

Christopher De Sa, Albert Cu, Rohan Puttagunta, Christopher Ré, Atri Rudra
2018 Proceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms  
We leave the study of approximation and numerical stability (which are important for computation over real/complex numbers) for future work. 2 Furthermore over any infinite field F, non-linear operations  ...  Finally, we show how applications in areas such as multipoint evaluations of multivariate polynomials can be reduced to problems involving low recurrence width matrices. 1 This is in terms of operations  ...  We design a simple and general near-linear-operation matrix-vector multiplication algorithm for low recurrence width matrices, hence capturing these previously disparate classes.  ... 
doi:10.1137/1.9781611975031.69 dblp:conf/soda/SaGPRR18 fatcat:ca66zs6rlfeg7mizl62jcvdpgm

A genetic algorithm for computing the k-error linear complexity of cryptographic sequences

A. Alecu, A. M. Salagean
2007 2007 IEEE Congress on Evolutionary Computation  
Efficient algorithms for computing the kerror linear complexity of a sequence over a finite field only exist for sequences of period equal to a power of the characteristic of the field.  ...  Such sequences should therefore have a large linear complexity and also a large k-error linear complexity.  ...  Chris Hinde for the useful discussions on the subject of this paper.  ... 
doi:10.1109/cec.2007.4424935 dblp:conf/cec/AlecuS07 fatcat:tbddodbi25f3zc4ntxsldymuji

Truncated orthogonal expansions of recurrent signals: equivalence to a linear time-variant periodic filter

S. Olmos, J. Garcia, R. Jane, P. Laguna
1999 IEEE Transactions on Signal Processing  
In this correspondence, we show that orthogonal expansions of recurrent signals like electrocardiograms (ECG's) with a reduced number of coefficients is equivalent to a linear time-variant periodic filter  ...  However, the new algorithm deals with multiple inputs and multiple outputs (MIMO's) and uses a Levenberg-Marquardt method for the minimization of the cost function.  ...  We can see that the main frequency components of QRS complex [22] [Fig. 9(b)] are well represented, whereas other waveforms like the P wave and the ST segment [ Fig. 10 .Fig. 11 . 1011 For example, for  ... 
doi:10.1109/78.796456 fatcat:xxwtuwsgajbltmcp576bjte4qi

Analysis of Work-Stealing and Parallel Cache Complexity [article]

Yan Gu, Zachary Napier, Yihan Sun
2021 arXiv   pre-print
Our second and main contribution is some new parallel cache complexity for algorithms using the RWS scheduler.  ...  Our new analysis decouples the span from the analysis of the parallel cache complexity. This allows us to show new parallel cache bounds for a list of classic algorithms.  ...  While the results in these papers are reasonably good for algorithms with low (polylogarithmic) span, the bounds for parallel overhead can be significant for algorithms with linear or super-linear span  ... 
arXiv:2111.04994v1 fatcat:yjvrumbacjdcnifdf6qvwwblmq

Multiple Recurrences and the Associated Matrix Structures Stemming From Normal Matrices

Clara Mertens, Raf Vandebril
2014 SIAM Journal on Numerical Analysis  
Moreover, the matrix building blocks allow us to also derive multiple recurrence relations for B-normal matrices, normal matrices whose eigenvalues lie on the union of curves in the complex plane, normal  ...  In this article we first review classical results on short multiple recurrences for normal matrices whose Hermitian conjugate can be written as a "low degree" rational function of the matrix.  ...  We are especially thankful for their input concerning the isometric Arnoldi algorithm and its variants for shifted unitary matrices.  ... 
doi:10.1137/120903555 fatcat:m5bi5c377ncvzdhj7hjw6gqmlm

On Linear Complexity of Binary Sequences Generated Using Matrix Recurrence Relation Defined Over Z4

S Ramesh, K.N Haribhat, R Murali
2010 International Journal of Distributed and Parallel systems  
This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z 4.  ...  In this paper a linear recursion sequence of matrices or vectors over Z 4 is generated from which random binary sequence is obtained. It is shown that such sequences have large linear complexity.  ...  Also LFSR can be easily implemented both in hardware and software.However m-sequences have low linear complexity. For an m-sequence of length 2 n -1 the linear complexity is n.  ... 
doi:10.5121/ijdps.2010.1207 fatcat:kmzfaamqs5hppm6fmmvyv34du4

A Nonlinear Acoustic Echo Canceller For Hands-Free Telephony

A Bdellatif, Ben Rabaa, Rached Tourki
2000 Zenodo  
The linear subsection is a linear filter using a Fast Affine Projection Algorithm (FAP) [15] [16] [17] .  ...  FAP's key features include LMS like complexity and memory requirement (low), and RLS like convergence (fast) for the important case where the excitation signal is speech.  ... 
doi:10.5281/zenodo.37520 fatcat:rgmsklm62rd77fsrdidpj4yh5i

Page 8549 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
For a linear recurrent sequence (LRS) u over a commutative local ring R with identity and @(x;,...  ...  Petersburg) 2001k:94038 94A29 Shamir, Gil I. (1-NDM-E; Notre Dame, IN); Costello, Daniel J., Jr. (1-NDM-E; Notre Dame, IN) Asymptotically optimal low-complexity sequential lossless coding for piecewise-stationary  ... 
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