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Some remarks on numerical iterations in a symbolic manipulation system

Aik-Koan Heng
<span title="">1990</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ezljl2d3lzga5efenbxdvvfcpa" style="color: black;">Journal of symbolic computation</a> </i> &nbsp;
Real numbers are represented as rational numbers in a symbolic manipulation system.  ...  The advantage of using this type of system performing numerical iterations is to reduce the roundoff error of operations.  ...  Acknowledgement I would like to express my gratitude to HITACHI foundation for supporting my sabbatical leave in Tokyo, and my host scientist Prof. Yasumasa KANADA for his critique of this paper.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0747-7171(08)80042-9">doi:10.1016/s0747-7171(08)80042-9</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5ew5gaywvze3filyrmwyncdkai">fatcat:5ew5gaywvze3filyrmwyncdkai</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170928084416/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/629/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS9zMDc0NzcxNzEwODgwMDQyOQ%3D%3D.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/3d/9f/3d9f4db09b52f684d4f245fb5ad06455e562d92a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/s0747-7171(08)80042-9"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Modified deflation algorithm for the solution of singular problems. I. A system of nonlinear algebraic equations

Takeo Ojika
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
In this paper a new method with symbolic and numerical manipulations, termed the modified deflation algorithm, is proposed for the singular root of a system of nonlinear algebraic equations.  ...  In addition it is often possible to obtain analytically the singular root from the new equations. In order to show the effectiveness of the present method two illustrative examples are solved.  ...  All the computations were done on the DEC-System 2020 of the Research Institute for Mathematical Sciences, Kyoto University, Kyoto, Japan.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-247x(87)90304-0">doi:10.1016/0022-247x(87)90304-0</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/pjbdidkfqfbuzfsf5cfwim3aym">fatcat:pjbdidkfqfbuzfsf5cfwim3aym</a> </span>
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Approximation of dynamical systems using s-systems theory

Laurent Tournier
<span title="">2005</span> <i title="ACM Press"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p5cu7ybzmnd3jpp7pphgogfzpi" style="color: black;">Proceedings of the 2005 international symposium on Symbolic and algebraic computation - ISSAC &#39;05</a> </i> &nbsp;
In this article we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system.  ...  This algorithm uses a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems).  ...  We will see an application of this algorithm on a biological example in dimension 14. We finally conclude with some remarks on our algorithm and some future works.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1073884.1073928">doi:10.1145/1073884.1073928</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/issac/Tournier05.html">dblp:conf/issac/Tournier05</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/o7jc75yphvd6phagz5i32ohshm">fatcat:o7jc75yphvd6phagz5i32ohshm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170809124239/http://www-sop.inria.fr/comore/personnel/Laurent.Tournier/Ssyst.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/fb/a0/fba02c6f52bd6f7ad33a05aea732c5414e103d8b.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/1073884.1073928"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Page 2676 of Mathematical Reviews Vol. , Issue 93e [page]

<span title="">1993</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;
Remark on: New directions and open problems in iteration theory [Forschungszentrum Graz, Graz, 1984; MR 86i:26004] by Gy.  ...  Reitberger, Some remarks about a controversy on the solution of Schréder’s functional equation (376-378); Maciej Sablik, On a problem of M. Hmissi (379-381); J. Smital, Solution of a problem by Prof.  ... 
<span class="external-identifiers"> </span>
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Digital Filter Design Using Computer Algebra Systems

Miroslav D. Lutovac, Jelena D. Ćertić, Ljiljana D. Milić
<span title="2009-06-20">2009</span> <i title="Springer Nature"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/c2au2pagvndhnnoq4ldjj6smp4" style="color: black;">Circuits, systems, and signal processing</a> </i> &nbsp;
The computer algebra systems successfully overcome some problems encountered in the traditional numeric-only approach.  ...  In this paper, we introduce an original approach to algorithm development and digital filter design using a computer algebra system.  ...  The use of computer algebra systems (CASs) and symbolic processing can help us gain insight into how some system works, although this system is preferred to experiment with numeric simulations.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/s00034-009-9119-2">doi:10.1007/s00034-009-9119-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tggsco4verb2jnhnm3u5ek7vty">fatcat:tggsco4verb2jnhnm3u5ek7vty</a> </span>
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A note on the integral formulation of Kumar and Sloan

J.I. Frankel
<span title="">1995</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
Finally, some remarks on the generalization of the method of Kumar and Sloan to higher-dimensional systems are offered.  ...  Symbolic computation is used in performing the numerous analytic manipulations leading to the establishment of the error estimates.  ...  Acknowledgements The work presented here was supported under a grant provided by the Department of Energy (DE-FG05-93ER25173).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(94)00071-3">doi:10.1016/0377-0427(94)00071-3</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/jy55jhvkbvcqvilcp3zc4cansq">fatcat:jy55jhvkbvcqvilcp3zc4cansq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190315181455/https://core.ac.uk/download/pdf/82302839.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/59/d6/59d6a755c4666be8feb92753176e126421f7e095.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0377-0427(94)00071-3"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Verifying Safety of Functional Programs with Rosette/Unbound [article]

Dmitry Mordvinov, Grigory Fedyukovich
<span title="2017-04-15">2017</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Rosette/Unbound is successfully evaluated on a set of non-trivial recursive and higher order functional programs.  ...  One of the key features of Rosette/Unbound is the ability to synchronize recursive computations over the same inputs allowing to verify programs that iterate over unbounded data streams multiple times.  ...  user code by adding some system routines' calls for tracking its execution.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1704.04558v1">arXiv:1704.04558v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/odsv3pnxdfa5zmzmsv4b2c2n5q">fatcat:odsv3pnxdfa5zmzmsv4b2c2n5q</a> </span>
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Page 363 of Mathematical Reviews Vol. , Issue 88a [page]

<span title="">1988</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;
Part of the proof is based upon numerical computation. It relies upon numerical integration of the equations, in some places, and upon symbolic manipulation programs to help algebraic manipulations.  ...  Closely related is the work of Blanchard on the symbolic dynam- ics of iterated cubics when the Julia set is disconnected.  ... 
<span class="external-identifiers"> </span>
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Derivation of Adams Method for the Numerical Solution of Ordinary Differential Equations Via Computer Algebra

Mustafa A.
<span title="">2017</span> <i title="Science Publishing Group"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xzng3bkx2jfvtkgeguyywsoqeq" style="color: black;">Applied and Computational Mathematics</a> </i> &nbsp;
In this paper, a well-known computer algebra system (CAS) was considered for the derivation of Numerical method for the solution of initial value problems.  ...  In particular, a review of Maple's functional role in the derivation of numerical methods was also presented.  ...  A brief report on the use of the symbolic manipulation language Maple, [4] , for construction of stochastic numerical schemes was also illustrated.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11648/j.acm.20170604.11">doi:10.11648/j.acm.20170604.11</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4uw2i6n4xbce3loxmg57kvbjom">fatcat:4uw2i6n4xbce3loxmg57kvbjom</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180720101132/http://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20170604.11.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/40/2f/402fc75dbfa0c19a6d5ee680567379cd2d838760.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11648/j.acm.20170604.11"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> Publisher / doi.org </button> </a>

Modified deflation algorithm for the solution of singular problems. II. Nonlinear multipoint boundary value problems

Takeo Ojika
<span title="">1987</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/7a65khxirfbfljbnqng5zzeslu" style="color: black;">Journal of Mathematical Analysis and Applications</a> </i> &nbsp;
Various kinds of iterative methods have been proposed for the solution of nonlinear multipoint boundary-value problems MPBVP's.  ...  In this paper an algorithm for the singular solution of nonlinear MPBVP's, which is an extension of the modified deflation algorithm for the singular root of nonlinear algebraic equations developed by  ...  All the computations were done on the DEC-System 2020 of the Research Institute for Mathematical Sciences of Kyoto University. Kyoto. Japan.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-247x(87)90305-2">doi:10.1016/0022-247x(87)90305-2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nks4ge7zqvdojl3ftcgttpkzjq">fatcat:nks4ge7zqvdojl3ftcgttpkzjq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170922100605/http://publisher-connector.core.ac.uk/resourcesync/data/elsevier/pdf/019/aHR0cDovL2FwaS5lbHNldmllci5jb20vY29udGVudC9hcnRpY2xlL3BpaS8wMDIyMjQ3eDg3OTAzMDUy.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/12/55/125543b88d67c4f2e25f0b9b6ba69c4bfd2a4a88.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/0022-247x(87)90305-2"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Hybrid manipulations for the solution of systems of nonlinear algebraic equations

Satoshi Watanabe
<span title="">1983</span> <i title="European Mathematical Publishing House"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/a7f55p6kqzhqzkkwln5cebjyai" style="color: black;">Publications of the Research Institute for Mathematical Sciences</a> </i> &nbsp;
Many methods by the numerical manipulation languages such as FORTRAN have been proposed so far for finding the numerical solution of a system of nonlinear algebraic equations given by (1.1) /(-r)=0, where  ...  x and f(x) are real ^/-dimensional vectors, and f(x) is defined to be twice continuously differentiable on a bounded region D in R n .  ...  Mitsui of Fukui University for many useful and valuable disccussions in the course of this work. He also would like to acknowledge to the reference for the remarks about Samanskii's works.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2977/prims/1195182438">doi:10.2977/prims/1195182438</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/p7oa32fczrh7pmwhr3q62rkf34">fatcat:p7oa32fczrh7pmwhr3q62rkf34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20160821175015/http://www.ems-ph.org/journals/show_pdf.php?issn=0034-5318&amp;vol=19&amp;iss=2&amp;rank=1" 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/8a/70/8a70459b4962b4574e4f3d63ef3fbee2aaf32d58.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.2977/prims/1195182438"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On an application of symbolic computation and computer graphics to root-finders: The case of multiple roots of unknown multiplicity

Ivan Petković, Beny Neta
<span title="">2016</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/av75skmu6neednu63f27tpk7qu" style="color: black;">Journal of Computational and Applied Mathematics</a> </i> &nbsp;
In particular, we state useful cubically convergent iterative sequences that find the exact multiplicity in a few iteration steps.  ...  By the use of computer algebra system Mathematica, we employ symbolic computation through several programs to construct and investigate algorithms which both determine a sought zero and its multiplicity  ...  The iterative formula (1) was derived in [22] and later in [21] using a different approach. In the latter paper some useful properties of this formula were presented. Remark 2.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.cam.2016.06.008">doi:10.1016/j.cam.2016.06.008</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/tnnyev27n5e2plwzdhmkjaonaa">fatcat:tnnyev27n5e2plwzdhmkjaonaa</a> </span>
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Geometrically-Aware Interactive Object Manipulation

Min-Hyung Choi, James F. Cremer
<span title="">2000</span> <i title="Wiley"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/p2lpq6bugfcqxk44anrm6yki4m" style="color: black;">Computer graphics forum (Print)</a> </i> &nbsp;
It is an efficient iterative algorithm, quadratically convergent, with each iteration bounded by O´nnz´Lµµ, where nnz´Lµ is the number of non-zeros in L, a Cholesky factor of a sparse matrix.  ...  This paper describes formulation and management of constraints, and a nonlinear optimization algorithm that together enable interactive geometrically aware manipulation of articulated objects.  ...  We thank Yinyu Ye and Xiong Zhang for helpful advice on the formulation and solution of optimization problems.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1467-8659.00388">doi:10.1111/1467-8659.00388</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/34lme2zhrzam7patdfs2lh5ca4">fatcat:34lme2zhrzam7patdfs2lh5ca4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20030713180717/http://graphics.cudenver.edu:80/~mhong/paper/cgf.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/79/17/791720a2ce4cbb6c77ceb837618b3fd8587866c9.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1111/1467-8659.00388"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

A toolbox for program manipulation and efficient code generation with an application to a problem in computer vision

Michael B. Monagan, Gladys Monagan
<span title="">1997</span> <i title="ACM Press"> Proceedings of the 1997 international symposium on Symbolic and algebraic computation - ISSAC &#39;97 </i> &nbsp;
We describe the design of a package for creating efficient numeric code.  ...  The tools for manipulating programs include automatic differentiation, code optimization, and the complexity analysis of a program.  ...  Introduction This paper is about how to design a facility within a computer algebra system (CAS), in this case Maple, to make it easy for a user of the system to create an efficient numeric code (often  ... 
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The February meeting of the American Mathematical Society

F. N. Cole
<span title="1918-05-01">1918</span> <i title="American Mathematical Society (AMS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/hjoli2j6qffdpaalkszryuidk4" style="color: black;">Bulletin of the American Mathematical Society</a> </i> &nbsp;
SOME REMARKABLE DETERMINANTS OF INTEGERS. BY PROFESSOR E. T. BELL. 1.  ...  When two surfaces are applicable to one another, in the correspondence thus established there is a unique conjugate system of curves on each surface corresponding to a conjugate system on the other.  ... 
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