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Low complexity algorithms for linear recurrences

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

doi:10.1145/1145768.1145781
dblp:conf/issac/BostanCSC06
fatcat:2eh2lnt7rbcsvjsrpfpwbuysci
*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*. ...##
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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. ...##
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Deep clustering of longitudinal data
[article]

2018
*
arXiv
*
pre-print

These methods provide a framework to model

arXiv:1802.03212v1
fatcat:t4ceogbunvhvhjlwye3lpjbxqu
*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. ...##
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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. ...##
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Nonlinear predictive control based on neural multi-models

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

doi:10.2478/v10006-010-0001-y
fatcat:cphqe7sxofdzbpam3iejj5nutq
*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. ...##
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On the numerical evaluation of linear recurrences

2003
*
Journal of Computational and Applied Mathematics
*

We present some remarks on the numerical evaluation of

doi:10.1016/s0377-0427(02)00565-4
fatcat:corz322or5ehdaqpuodfje7hse
*recurrence*relations. ... limit case of Jacobi-Sobolev polynomials, random*recurrences*and perturbed Gegenbauer polynomials. ... of*algorithms*with*low*computational*complexity*[10] . ...##
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Page 4072 of Mathematical Reviews Vol. , Issue 93g
[page]

1993
*
Mathematical Reviews
*

The authors consider a so-called “

*low*-*complexity**algorithm*”*for**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. ...##
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A Two-pronged Progress in Structured Dense Matrix Vector Multiplication
[chapter]

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

doi:10.1137/1.9781611975031.69
dblp:conf/soda/SaGPRR18
fatcat:ca66zs6rlfeg7mizl62jcvdpgm
*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. ...##
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A genetic algorithm for computing the k-error linear complexity of cryptographic sequences

2007
*
2007 IEEE Congress on Evolutionary Computation
*

Efficient

doi:10.1109/cec.2007.4424935
dblp:conf/cec/AlecuS07
fatcat:tbddodbi25f3zc4ntxsldymuji
*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. ...##
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Truncated orthogonal expansions of recurrent signals: equivalence to a linear time-variant periodic filter

1999
*
IEEE Transactions on Signal Processing
*

In this correspondence, we show that orthogonal expansions of

doi:10.1109/78.796456
fatcat:xxwtuwsgajbltmcp576bjte4qi
*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*...##
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Analysis of Work-Stealing and Parallel Cache Complexity
[article]

2021
*
arXiv
*
pre-print

Our second and main contribution is some new parallel cache

arXiv:2111.04994v1
fatcat:yjvrumbacjdcnifdf6qvwwblmq
*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 ...##
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Multiple Recurrences and the Associated Matrix Structures Stemming From Normal Matrices

2014
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SIAM Journal on Numerical Analysis
*

Moreover, the matrix building blocks allow us to also derive multiple

doi:10.1137/120903555
fatcat:m5bi5c377ncvzdhj7hjw6gqmlm
*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. ...##
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On Linear Complexity of Binary Sequences Generated Using Matrix Recurrence Relation Defined Over Z4

2010
*
International Journal of Distributed and Parallel systems
*

This paper discusses the

doi:10.5121/ijdps.2010.1207
fatcat:kmzfaamqs5hppm6fmmvyv34du4
*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. ...##
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A Nonlinear Acoustic Echo Canceller For Hands-Free Telephony

2000
*
Zenodo
*

The

doi:10.5281/zenodo.37520
fatcat:rgmsklm62rd77fsrdidpj4yh5i
*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. ...##
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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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