Filters








20,332 Hits in 7.9 sec

A Deterministic Algorithm to Compute Approximate Roots of Polynomial Systems in Polynomial Average Time

Pierre Lairez
<span title="2016-05-18">2016</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2joypbq7ubehha6yu7ylkxkoqa" style="color: black;">Foundations of Computational Mathematics</a> </i> &nbsp;
We describe a deterministic algorithm that computes an approximate root of n complex polynomial equations in n unknowns in average polynomial time with respect to the size of the input, in the Blum-Shub-Smale  ...  It rests upon a derandomization of an algorithm of Beltr\'an and Pardo and gives a deterministic affirmative answer to Smale's 17th problem.  ...  Acknowledgment I am very grateful to Peter Bürgisser for his help and constant support, and to Carlos Beltrán for having carefully commented this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-016-9319-7">doi:10.1007/s10208-016-9319-7</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6pwhizjagzfbhf6llvdiqvxdly">fatcat:6pwhizjagzfbhf6llvdiqvxdly</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190502185606/https://hal.archives-ouvertes.fr/hal-01178588/document" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a7/90/a790ab8ecee742b04379eec5c3206dfe940f75ea.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-016-9319-7"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Foreword

Teresa Krick, James Renegar
<span title="2015-01-09">2015</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2joypbq7ubehha6yu7ylkxkoqa" style="color: black;">Foundations of Computational Mathematics</a> </i> &nbsp;
Mike and Steve conjectured that on average, a root of a polynomial system can be approximated accurately in polynomial time, a conjecture finally settled affirmatively by Carlos Beltrán and Luis Pardo  ...  In the early 1980s, Mike began collaborating with Steve in investigating the computational complexity of algorithms for approximating roots of polynomials, initially for univariate polynomials and later  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-014-9234-8">doi:10.1007/s10208-014-9234-8</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bjau57ao6neb5muehdh6lm6ppq">fatcat:bjau57ao6neb5muehdh6lm6ppq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180726225503/https://link.springer.com/content/pdf/10.1007%2Fs10208-014-9234-8.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d6/f8/d6f843f1c3b51eac4b18431a71cd7cef182219e4.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s10208-014-9234-8"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Page 489 of Mathematical Reviews Vol. , Issue 98A [page]

<span title="">1998</span> <i title="American Mathematical Society"> <a target="_blank" rel="noopener" href="https://archive.org/details/pub_mathematical-reviews" style="color: black;">Mathematical Reviews </a> </i> &nbsp;
As evidence toward this conjecture, we show that if any polynomial-time algorithm can approximate the longest path to a ratio of 29°“), for any e > 0, then NP has a quasi-polynomial deterministic time  ...  We then show that no polynomial- time algorithm can find a constant factor approximation to the longest-path problem unless P = NP.  ... 
<span class="external-identifiers"> </span>
<a target="_blank" rel="noopener" href="https://archive.org/details/sim_mathematical-reviews_1998-01_98a/page/489" title="read fulltext microfilm" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Archive [Microfilm] <div class="menu fulltext-thumbnail"> <img src="https://archive.org/serve/sim_mathematical-reviews_1998-01_98a/__ia_thumb.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a>

Deterministic wavelet thresholding for maximum-error metrics

Minos Garofalakis, Amit Kumar
<span title="">2004</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xtq6wnwaszaebg4qf7aw6mllwi" style="color: black;">Proceedings of the twenty-third ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems - PODS &#39;04</a> </i> &nbsp;
We introduce an optimal low polynomial-time algorithm for one-dimensional wavelet thresholding -our algorithm is based on a new Dynamic-Programming (DP) formulation, and can be employed to minimize the  ...  Unfortunately, directly extending our one-dimensional DP algorithm to multi-dimensional wavelets results in a super-Permission to make digital or hard copies of all or part of this work for personal or  ...  We use this idea to devise a polynomial-time (1 + )-approximation scheme. Given a threshold parameter τ > 0, we define a truncated DP algorithm as follows.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1055558.1055582">doi:10.1145/1055558.1055582</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/pods/GarofalakisK04.html">dblp:conf/pods/GarofalakisK04</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3run2fuxp5bxxawt4aoqrhqzbe">fatcat:3run2fuxp5bxxawt4aoqrhqzbe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20090115233540/http://www.softnet.tuc.gr/~minos/Papers/pods04-cam.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/35/b1/35b1b6a58d1c173306424627c573f72a51513138.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1055558.1055582"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

An Explicit VC-Theorem for Low-Degree Polynomials [chapter]

Eshan Chattopadhyay, Adam Klivans, Pravesh Kothari
<span title="">2012</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We also give the first hardness result for this problem and show that the existence of a poly(n k , |X|, 1/ǫ)-time algorithm for deterministically constructing ǫ-approximations for circuits of size n k  ...  We show that for any X ⊆ R n and any Boolean function class C that is uniformly approximated by degree k, low-weight polynomials, an ǫ-approximation S can be be constructed deterministically in time poly  ...  Hardness of Constructing ǫ-Approximations In this section we show that an efficient deterministic algorithm to compute an ǫ-approximation (or a hard function) for the class of polynomial size circuits  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-32512-0_42">doi:10.1007/978-3-642-32512-0_42</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qef3ghouf5dihm6ttda42b7efe">fatcat:qef3ghouf5dihm6ttda42b7efe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190218225617/http://pdfs.semanticscholar.org/149d/9a2d43eec757040bc1eab884c382d1b2cc51.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/14/9d/149d9a2d43eec757040bc1eab884c382d1b2cc51.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-32512-0_42"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

A Bluff-and-Fix Algorithm for Polynomial Chaos Methods [chapter]

Laura Lyman, Gianluca Iaccarino
<span title="">2020</span> <i title="Springer International Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
The strategy is to express the resulting stochastic solution using M + 1 terms of a polynomial chaos expansion and then derive and solve a deterministic, coupled system of PDEs with standard numerical  ...  Stochastic Galerkin methods can be used to approximate the solution to a differential equation in the presence of uncertainties represented as stochastic inputs or parameters.  ...  This representation has its roots in the work of Wiener [7] , who expressed a Gaussian process as an infinite series of Hermite polynomials.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-50436-6_55">doi:10.1007/978-3-030-50436-6_55</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2kpxtgdm7fehpdaunv24lwcebe">fatcat:2kpxtgdm7fehpdaunv24lwcebe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200712201408/https://link.springer.com/content/pdf/10.1007%2F978-3-030-50436-6_55.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b5/5e/b55ee5b0bd4b2e94c7a9e4b7a61350be35f813fb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-030-50436-6_55"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

The Module Structure of ARMAX Systems

Ivan Markovsky, Jan C. Willems, Bart De Moor
<span title="">2006</span> <i title="IEEE"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wjd7b2sxyfahnaei4xvi46vwsu" style="color: black;">Proceedings of the 45th IEEE Conference on Decision and Control</a> </i> &nbsp;
We propose an ARMAX identification algorithm, which has three steps: first compute the deterministic part of the system via the orthogonalizers, then the AR part, which also has a module structure, and  ...  Computing a module basis for the orthogonalizers is a deterministic identification problem.  ...  polynomial time algorithms of [7] or [8] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2006.377656">doi:10.1109/cdc.2006.377656</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/cdc/MarkovskyWM06.html">dblp:conf/cdc/MarkovskyWM06</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ojmeavucp5g3jcguwqbukgigpm">fatcat:ojmeavucp5g3jcguwqbukgigpm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170811070217/http://homes.esat.kuleuven.be/~jwillems/Articles/ConferenceArticles/2006/2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/90/47/9047c50f249fbf274785dd8cff2f9ba5f43d9af7.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/cdc.2006.377656"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> ieee.com </button> </a>

A Faster Solution to Smale's 17th Problem I: Real Binomial Systems [article]

Grigoris Paouris, Kaitlyn Phillipson, J. Maurice Rojas
<span title="2019-01-28">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We give a deterministic algorithm that finds a real approximate root (or correctly decides there are none) using just O(n^2((n)+_i d_i)) arithmetic operations on average.  ...  We also discuss briefly the obstructions to maintaining average-case time polynomial in n_i d_i when F has more terms.  ...  ACKNOWLEDGEMENTS We humbly thank REU students Caleb Bugg and Paula Burkhardt for important discussions on preliminary versions of this work.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.09739v1">arXiv:1901.09739v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/k3k4hubsq5c23f4syikndvkqdq">fatcat:k3k4hubsq5c23f4syikndvkqdq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200929165657/https://arxiv.org/pdf/1901.09739v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e6/08/e60802604dca85945ffeb68956bd20b1eee91282.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1901.09739v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Four Integer Factorization Algorithms [article]

N. A. Carella
<span title="2010-08-31">2010</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The running time complexity of these algorithms ranges from deterministic exponential time complexity O(N^(1/2)) to heuristic and unconditional logarithmic time complexity O((log N)^c), c > 0 constant.  ...  The theoretical aspects of four integer factorization algorithms are discussed in details in this note.  ...  On average, the norm of a small vector in a lattice is approximated by the geometric mean, that is, n n i L V / 1 2 / 1 2 ) det( γ ≤ .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1003.3261v3">arXiv:1003.3261v3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hxqhnl7yq5fivjurgr2466hluu">fatcat:hxqhnl7yq5fivjurgr2466hluu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200911045825/https://arxiv.org/ftp/arxiv/papers/1003/1003.3261.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f3/6a/f36a99f277ef89d20eb98f3ecc9934dae32ac01f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1003.3261v3" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Efficient uncertainty quantification with the polynomial chaos method for stiff systems

Haiyan Cheng, Adrian Sandu
<span title="">2009</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/olxojxefbfaxbjvmwjvhp47sra" style="color: black;">Mathematics and Computers in Simulation</a> </i> &nbsp;
In the Galerkin approach, we propose a modification in the implicit time stepping process using an approximation of the Jacobian matrix to reduce the computational cost.  ...  When stiff systems are considered, implicit numerical integration requires the solution of a nonlinear system of equations at every time step.  ...  But at the same time, the computation time is increased due to the increase of the number of the deterministic runs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.matcom.2009.05.002">doi:10.1016/j.matcom.2009.05.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4ih3cwechzftbkk64r4w4dno2a">fatcat:4ih3cwechzftbkk64r4w4dno2a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20100606140901/http://eprints.cs.vt.edu/archive/00000978/01/UQstiff_report.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/60/78/607804c93609e614ea5b2324b4666c3f5ccbc7e0.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.matcom.2009.05.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Efficiently Computing the Density of Regular Languages [chapter]

Manuel Bodirsky, Tobias Gärtner, Timo von Oertzen, Jan Schwinghammer
<span title="">2004</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We present an algorithm that computes the number of accumulation points of (fm) in polynomial time, if the regular language L is given by a finite deterministic automaton, and can then also efficiently  ...  A regular language L is called dense if the fraction fm of words of length m over some fixed signature that are contained in L tends to one if m tends to infinity.  ...  To approximate the values at the roots of unity up to n bits we need O(n 2 log n) time.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-24698-5_30">doi:10.1007/978-3-540-24698-5_30</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bukd7lwxa5behbvzvaiyq5saqm">fatcat:bukd7lwxa5behbvzvaiyq5saqm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20130107225440/http://www.lix.polytechnique.fr/~bodirsky/publications/Pregdens.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a9/be/a9be072d977e0e61b55c100bdc6d836596dbbd96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-540-24698-5_30"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Intrinsic Near Quadratic Complexity Bounds for Real Multivariate Root Counting [chapter]

J. Maurice Rojas
<span title="">1998</span> <i title="Springer Berlin Heidelberg"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/2w3awgokqne6te4nvlofavy5a4" style="color: black;">Lecture Notes in Computer Science</a> </i> &nbsp;
We give a new algorithm, with three versions, for computing the number of real roots of a system of n polynomial equations in n unknowns.  ...  The rst version is of Monte Carlo type and, neglecting logarithmic factors, runs in time quadratic in the average number of complex roots of a closely related system.  ...  A Simple Example of Our Algorithm Suppose one would like to count the number of real roots of the following bivariate polynomial system: f 1 (x; y) = 1 ? 2x 8 y 2 ?  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-68530-8_11">doi:10.1007/3-540-68530-8_11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fdw7eef5h5cbjp2uxljgtqlzy4">fatcat:fdw7eef5h5cbjp2uxljgtqlzy4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190228090927/http://pdfs.semanticscholar.org/8f83/172cf69d9aca8577511ea13f0570e20cfafb.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/8f/83/8f83172cf69d9aca8577511ea13f0570e20cfafb.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/3-540-68530-8_11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

On the Complexity of Diophantine Geometry in Low Dimensions [article]

J. Maurice Rojas
<span title="1998-11-13">1998</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Better still, we show that the truth of the Generalized Riemann Hypothesis implies that detecting roots in Q^n for the polynomial systems in (I) can be done via a two-round Arthur-Merlin protocol, i.e.  ...  A practical point of interest is that the aforementioned Diophantine problems should perhaps be avoided in the construction of crypto-systems.  ...  So via [Coh93] , a putative root of F mod p can indeed be verified in polynomial time. So we indeed need only one call to an NP oracle. Our algorithm is thus indeed an AM algorithm.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9811088v1">arXiv:math/9811088v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/2p7qxmzr6ra5hjimaajaocqspu">fatcat:2p7qxmzr6ra5hjimaajaocqspu</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-math9811088/math9811088.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/math/9811088v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

On the complete instability of interval polynomials

F. Dabbene, B.T. Polyak, R. Tempo
<span title="">2007</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/b4jbqehv5vdltfaa3oor24oddm" style="color: black;">Systems &amp; control letters (Print)</a> </i> &nbsp;
That is, the objective is to check if all polynomials in the family are unstable. If not, a subsequent goal is to find a stable polynomial.  ...  The second contribution of this paper is to provide a probability-one estimate of the volume of stable polynomials. These results are based on a combination of deterministic and randomized methods.  ...  A different approach followed in this literature is to develop efficient polynomial-time randomized algorithms for computing the volume of convex bodies, see [5] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.sysconle.2006.11.002">doi:10.1016/j.sysconle.2006.11.002</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wouesjp3uncmxizhkr2n3zn62q">fatcat:wouesjp3uncmxizhkr2n3zn62q</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170810081315/http://www.nsc.ru/interval/Library/Thematic/IAControl/CompleteInstability.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d7/89/d78946efe4db4613bf5b7dbbb843342f3a732e96.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.sysconle.2006.11.002"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Sublinear-Time Algorithms for Monomer-Dimer Systems on Bounded Degree Graphs [article]

Marc Lelarge, Hang Zhou
<span title="2013-09-04">2013</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We show that our algorithm approximates the probability for a vertex to be covered by a matching, sampled according to this Gibbs distribution, in a near-optimal sublinear time.  ...  We extend our results to approximate the average size and the entropy of such a matching within an additive error with high probability, where again the query complexity is polynomial in 1/ϵ and the lower  ...  The authors acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-11-JS02-005-01 (GAP project).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1208.3629v5">arXiv:1208.3629v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ewl7embvbcn5odnhhbbyaqypq">fatcat:5ewl7embvbcn5odnhhbbyaqypq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200827090555/https://arxiv.org/pdf/1208.3629v5.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/79/46/794605ebacac47242c0544845e36b969d9bdf37d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1208.3629v5" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
&laquo; Previous Showing results 1 &mdash; 15 out of 20,332 results