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Page 24 of Mathematical Reviews Vol. , Issue 88a [page]

1988 Mathematical Reviews  
Let p be a prime, let Z,» be the ring of integers mod p” and let R(p") be its group of units. Let S,(p) be the affine group of de- gree one over Zp». So S,(p) = (5 ) :x € R(p"), y € Zpn}.  ...  “The study of polynomial-time algorithms for groups has only recently begun.  ... 

On the Convergence of Schur Parameters for a Toeplitz Matrix with a Meromorphic Symbol [chapter]

Adhemar Bultheel
1986 Operator Theory: Advances and Applications  
The limit behavior of Schur parameters is investigated when they are associated to Toeplitz matrices of growing size whose entries are the Laurent coefficients of a meromorphic function.  ...  Most remarkable is that such functions can be characterized by a sequence of parameters that can be obtained from its Fourier coefficients by some elegant algorithm.  ...  This gives the possibility to find the zeros of F (z) that are in Iz I < p. The Rutishauser polynomials have then to be defined by Pn(m,m-k-l)(z) = zPn(m,m-k)(z) -an(~l-k-l)Pn('!:.  ... 
doi:10.1007/978-3-0348-5483-2_6 fatcat:rjts2vywwnfdhokelln63zo6xy

The average number of critical rank-one approximations to a tensor [article]

Jan Draisma, Emil Horobet
2015 arXiv   pre-print
Motivated by the many potential applications of low-rank multi-way tensor approximations, we set out to count the rank-one tensors that are critical points of the distance function to a general tensor  ...  As this count depends on v, we average over v drawn from a Gaussian distribution, and find formulas that relates this average to problems in random matrix theory.  ...  We thank the authors of that paper, as well as our Eindhoven colleague Rob Eggermont, for several stimulating discussions on the topic of this paper.  ... 
arXiv:1408.3507v2 fatcat:es7ewbibyfhifnxitcdjc2bkze

The average number of critical rank-one approximations to a tensor

Jan Draisma, Emil Horobeţ
2016 Linear and multilinear algebra  
We thank the authors of that paper, as well as our Eindhoven colleague Rob Eggermont, for several stimulating discussions on the topic of this paper.  ...  This paper fits in the research programme laid out in [DHO`13], which asks for Euclidean distance degrees of algebraic varieties arising in applications.  ...  This function is invariant under conjugating C with an orthogonal matrix, and as a consequence, the joint density of the ordered tuple pλ 2 ď . . . ď λ n q of eigenvalues of C equals Zpn´1qf n´1 pΛq ź  ... 
doi:10.1080/03081087.2016.1164660 fatcat:53z33mshtfbp3muchvrzw3jrau

Quantum computational algorithm for hidden symmetry subgroup problems on semi-direct product of cyclic groups [article]

Jeong San Kim, Eunok Bae, Soojoon Lee
2013 arXiv   pre-print
We characterize the algebraic structure of semi-direct product of cyclic groups, _N_p, where p is an odd prime number which does not divide q-1 for any prime factor q of N, and provide a polynomial-time  ...  quantum computational algorithm solving hidden symmetry subgroup problem of the groups.  ...  For a given oracle function f over M , which hides some subgroup H of G by symmetries, we construct a suitable function f HSP over G, which hides H.  ... 
arXiv:1307.1183v1 fatcat:ijh6ussugbg2ndnyrg2vgsnz3m

Moment problems and orthogonal functions

A. Bultheel, P. González-Vera, E. Hendriksen, O. Njåstad
1993 Journal of Computational and Applied Mathematics  
Let {cy,} be an arbitrary given sequence of not necessarily distinct points in D, and let {w,} be a given sequence of numbers.  ...  These problems are closely related to the theory of SzegB polynomials, i.e., orthogonal polynomials on the unit circle T = {z: 121 = 1).  ...  They are also related to the theory of Schur functions and various variants of the famous Schur algorithm.  ... 
doi:10.1016/0377-0427(93)90315-3 fatcat:exib5triqngizl2z74qusia36i

Channel Estimation Algorithms Comparison for Multiband-OFDM

Raffaello Tesi, Matti Hamalainen, Jari Iinatti
2006 2006 IEEE 17th International Symposium on Personal, Indoor and Mobile Radio Communications  
The algorithms used here are based on the least squares (LS) and the linear minimum mean-square error (LMMSE) approaches supported by linear and cubic interpolation, and an IFFT-based time channel estimation  ...  In frequency domain algorithms, phase compensation is also taken into account.  ...  The authors would like to thank all the sponsors for their support and Chalmers University of Technology, Sweden, for cooperation in the multiband-OFDM simulator development. VI REFERENCES  ... 
doi:10.1109/pimrc.2006.254397 dblp:conf/pimrc/TesiHI06 fatcat:t4n2p3dnyra5rd7vaw2tmht3dm

VISTA data flow system: overview

James P. Emerson, Mike J. Irwin, Jim Lewis, Simon Hodgkin, Dafydd Evans, Peter Bunclark, Richard McMahon, Nigel C. Hambly, Robert G. Mann, Ian Bond, Eckhard Sutorius, Michael Read (+3 others)
2004 Optimizing Scientific Return for Astronomy through Information Technologies  
Handling the data rates on a nightly basis, and the volumes of survey data accumulated over time each present new challenges.  ...  the quality of the data acquired, removal of instrumental artefacts, astrometric and photometric calibration, to accessibility of curated and user-specified data products in the context of the Virtual  ...  System (WCS) using the Zenithal polynomial (ZPN) projection 14 .  ... 
doi:10.1117/12.551582 fatcat:zmiwsn5oivfetcehjjjozc6eq4

Stochastic heavy ball

Sébastien Gadat, Fabien Panloup, Sofiane Saadane
2018 Electronic Journal of Statistics  
the iterations of the algorithm.  ...  This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout  ...  Finding the minimum of a function f over a set Ω with an iterative procedure is very popular among numerous scientific communities and has many applications in optimization, image processing, economics  ... 
doi:10.1214/18-ejs1395 fatcat:mwdpidfwajhtvg2bjflu5v2owq

Stochastic Heavy Ball [article]

Sébastien Gadat and Fabien Panloup and Sofiane Saadane
2016 arXiv   pre-print
the iterations of the algorithm.  ...  This work provides an in-depth description of the stochastic heavy-ball method, which is an adaptation of the deterministic one when only unbiased evalutions of the gradient are available and used throughout  ...  Introduction Finding the minimum of a function f over a set Ω with an iterative procedure is very popular among numerous scientific communities and has many applications in optimization, image processing  ... 
arXiv:1609.04228v2 fatcat:4c2o7baaujaw3ltjj45dh4hqla

Lectures on exceptional orthogonal polynomials and rational solutions to Painlevé equations [article]

David Gómez-Ullate, Robert Milson
2019 arXiv   pre-print
They summarize the basic results and construction of exceptional poynomials, developed over the past ten years.  ...  Some of the material presented here (Sturm-Liouville operators, classical orthogonal polynomials, Darboux-Crum transformations, etc.) are classical and can be found in many textbooks, while some results  ...  Polynomials and Applications, Duala (Cameroon), where these lectures were first taught.  ... 
arXiv:1912.07597v1 fatcat:rfiwohmpnrhnvamwcofuuhlamy

A property of interpolational spline functions

A. A. Ligun
1981 Ukrainian Mathematical Journal  
aplinea; the polynomial splines are obtained if p (D) = Dn. n There is an extensive literature on the problem of interpolation by means of polynomial splines. If the knots of the interpolating !  ...  Sectien 1.3 gives the definition of an of some particular function, tagether with the definitions such as cardinal !-splines and perfect Lsplines.  ...  Then A is interpreted as an algorithm and A(g) is considered to be an estimate for pk(D)f(O).  ... 
doi:10.1007/bf01091990 fatcat:aje7n5hhr5dp7ahx6oruwsv6oq

Convergence of adaptive discontinuous Galerkin methods (corrected version of [Math. Comp. 87 (2018), no. 314, 2611–2640]) [article]

Christian Kreuzer, Emmanuil H. Georgoulis
2020 arXiv   pre-print
Another key feature of the presented result is, that it holds for penalty parameters only necessary for the standard analysis of the respective scheme.  ...  The analysis is based on a quasi interpolation into a newly developed limit space of the adaptively created non-conforming discrete spaces, which enables to generalise the basic convergence result for  ...  Acknowledgement We thank the anonymous referee of the paper [DGK19] for finding a highly nontrivial counterexample to the first statement in [DGK19, Lemma 11], which lead to this corrected version of  ... 
arXiv:1909.12665v2 fatcat:2epb7ahtcjgxhfjcnjwgpvlzz4

Harmonic analysis and spectral estimation

John J. Benedetto
1983 Journal of Mathematical Analysis and Applications  
An example of technique is Wiener's Tauberian theorem; an example of point of view is thinking of spectral estimation in terms of the uniqueness theory associated with the work of Levinson and Beurling  ...  Section I contains preliminaries including an outline of generalized harmonic analysis.  ...  of my algorithm:  ... 
doi:10.1016/0022-247x(83)90164-6 fatcat:6omuiqu37ngojmvrwyldabqxya

Null Decomposition of Trees [article]

Daniel A. Jaume, Gonzalo Molina
2017 arXiv   pre-print
Let T be a tree, we show that the null space of the adjacency matrix of T has relevant information about the structure of T.  ...  We introduce the Null Decomposition of trees, and use it in order to get formulas for independence number and matching number of a tree.  ...  We gratefully acknowledge the many helpful suggestions of Adrián Pastine during the preparation of the paper.  ... 
arXiv:1708.00934v1 fatcat:vp6gs5pizvclvbhdf4p6ngtiia
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