Search Results - "Polynomials in real and complex fields: factorization"

Sur l'irréductibilité d'une classe des polynômes. I

Authors: Györy, K.

Source: Publicationes Mathematicae Debrecen. 18:289-307

Subject Terms: Polynomials in real and complex fields: factorization, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences, Polynomials in general fields (irreducibility, etc.), Polynomials in number theory

File Description: application/xml

Access URL: https://zbmath.org/3396043
https://zbmath.org/3425732

On the Greatest Common Divisor of Two Univariate Polynomials, I: On the greatest common divisor of two univariate polynomials. II

Authors: A. Schinzel

Source: Acta Arithmetica. 98:95-106

Subject Terms: polynomial, greatest common divisor, trinomial, number of terms, Polynomials in real and complex fields: factorization, Special polynomials in general fields, 0101 mathematics, 01 natural sciences, degree

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/83164?download.pdf
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa98-1-6
https://ui.adsabs.harvard.edu/abs/2001AcAri..98...95S/abstract
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/98/1/83164/on-the-greatest-common-divisor-of-two-univariate-polynomials-ii
https://eudml.org/doc/279332
https://www.impan.pl/shop/publication/transaction/download/product/83164?download.pdf
http://ebooks.cambridge.org/ref/id/CBO9780511542961A027

New resultant inequalities and complex polynomial factorization

Authors: Victor Y. Pan

Source: Lecture Notes in Computer Science ISBN: 3540555536

Subject Terms: computational complexity, parallel computing, polynomials, Analysis of algorithms and problem complexity, randomized algorithms, approximate factorization, 1. No poverty, Polynomials in real and complex fields: factorization, Parallel numerical computation, deterministic algorithm, 0102 computer and information sciences, 01 natural sciences, Complexity and performance of numerical algorithms, monic univariate polynomial, probabilistic estimates, polynomial factorization, 0103 physical sciences, zeros, Computational aspects of field theory and polynomials, complex field, resultant

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Access URL: https://dblp.uni-trier.de/db/conf/istcs/istcs1992.html#Pan92
https://locus.siam.org/doi/abs/10.1137/S0097539792235712
https://link.springer.com/chapter/10.1007/BFb0035172
https://dblp.uni-trier.de/db/journals/siamcomp/siamcomp23.html#Pan94
https://rd.springer.com/chapter/10.1007/BFb0035172
https://link.springer.com/content/pdf/10.1007%2FBFb0035172.pdf
https://epubs.siam.org/doi/abs/10.1137/S0097539792235712

An efficient resultant for determining reciprocal zeros in polynomials

Authors: H.J. Orchard Alan N. Willson

Source: Linear Algebra and its Applications. 411:309-327

Subject Terms: Resultant, Numerical Analysis, Algebra and Number Theory, Eliminant, 0202 electrical engineering, electronic engineering, information engineering, Polynomials in real and complex fields: factorization, Reciprocal zeros, Discrete Mathematics and Combinatorics, Geometry and Topology, 02 engineering and technology, 0101 mathematics, 01 natural sciences

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Access URL: https://zbmath.org/2235536
https://doi.org/10.1016/j.laa.2004.08.024
http://www.sciencedirect.com/science/article/pii/S0024379504003878
https://core.ac.uk/display/82272494
https://www.sciencedirect.com/science/article/pii/S0024379504003878

A generalization of Mason?s theorem for four polynomials: A generalization of Mason's theorem for four polynomials

Authors: H. Teimoori M. Bayat

Source: Elemente der Mathematik. 59:23-28

Subject Terms: roots of polynomials, Polynomials in real and complex fields: factorization, 06 humanities and the arts, 0101 mathematics, 0603 philosophy, ethics and religion, Higher degree equations, Fermat's equation, 01 natural sciences

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Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=59&iss=1&rank=3
https://zbmath.org/2102275
https://doi.org/10.1007/s00017-001-0203-2
https://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=59&iss=1&rank=3
https://www.ems-ph.org/doi/10.1007/s00017-001-0203-2
https://link.springer.com/article/10.1007/s00017-001-0203-2

Effective Fast Algorithms for Polynomial Spectral Factorization: Effective fast algorithms for polynomial spectral factorization

Authors: BINI, DARIO ANDREA G. FIORENTINO GEMIGNANI, LUCA et al.

Source: Numerical Algorithms. 34:217-227

Subject Terms: convergence, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), polynomial factorization, Graeffe method, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Laurent polynomial inversion, Numerical computation of solutions to single equations, spectral factorization, 0101 mathematics, numerical experiments, the Toeplitz matrix, 01 natural sciences

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Access URL: https://dblp.uni-trier.de/db/journals/na/na34.html#BiniFGM03
http://ui.adsabs.harvard.edu/abs/2003NuAlg..34..217B/abstract
https://doi.org/10.1023/B:NUMA.0000005364.00003.ea
https://link.springer.com/article/10.1023/B%3ANUMA.0000005364.00003.ea
https://arpi.unipi.it/handle/11568/187560
https://link.springer.com/content/pdf/10.1023/B:NUMA.0000005364.00003.ea.pdf
https://hdl.handle.net/11568/187560
https://doi.org/10.1023/B:NUMA.0000005364.00003.ea

The Equation f(X) = f(Y) in Rational Functions X = X(t), Y = Y(t): The equation \(f(X) = f(Y)\) in rational functions \(X = X(t)\), \(Y = Y(t)\)

Authors: Roberto Maria Avanzi Umberto Zannier

Source: Compositio Mathematica. 139:263-295

Subject Terms: Special algebraic curves and curves of low genus, diophantine equations, Curves of arbitrary genus or genus \(\ne 1\) over global fields, equations with rational functions as solutions, Polynomials in real and complex fields: factorization, reducibility, Higher degree equations, Fermat's equation, Polynomials in general fields (irreducibility, etc.), Polynomials in number theory, Polynomials (irreducibility, etc.)

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Access URL: https://www.cambridge.org/core/services/aop-cambridge-core/content/view/A7E2610BF5F9E8124BD2E710C4257F5A/S0010437X03100735a.pdf/div-class-title-the-equation-span-class-italic-f-span-span-class-italic-x-span-span-class-italic-f-span-span-class-italic-y-span-in-rational-functions-span-class-italic-x-span-span-class-italic-x-span-span-class-italic-t-span-span-class-italic-y-span-span-class-italic-y-span-span-class-italic-t-span-div.pdf
https://www.cambridge.org/core/journals/compositio-mathematica/article/equation-fx-fy-in-rational-functions-x-xt-y-yt/A7E2610BF5F9E8124BD2E710C4257F5A
https://link.springer.com/article/10.1023/B:COMP.0000018136.23898.65

On One Method for Factorization of Algebraic Polynomials: On one method for factorization of algebraic polynomials

Authors: B. M. Podlevs'kyi

Source: Ukrainian Mathematical Journal. 55:1472-1479

Subject Terms: algorithm, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), factorisation, 0103 physical sciences, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Numerical computation of solutions to single equations, multiple root, 0101 mathematics, 01 natural sciences, algebraic polynomial

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Access URL: https://zbmath.org/2210452
https://doi.org/10.1023/b:ukma.0000018008.76465.3e
https://link.springer.com/article/10.1023/B%3AUKMA.0000018008.76465.3e

Extremal properties of outer polynomial factors

Authors: Scott McCullough

Source: Proceedings of the American Mathematical Society. 132:815-825

Subject Terms: extremal property, outer factor, Factorization theory (including Wiener-Hopf and spectral factorizations) of linear operators, Polynomials in real and complex fields: factorization, 0101 mathematics, monic polynomial, Linear operator methods in interpolation, moment and extension problems, 01 natural sciences

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Access URL: https://www.ams.org/proc/2004-132-03/S0002-9939-03-07122-3/S0002-9939-03-07122-3.pdf
https://zbmath.org/2023424
https://doi.org/10.1090/s0002-9939-03-07122-3
https://www.jstor.org/stable/1194702
https://www.ams.org/journals/proc/2004-132-03/S0002-9939-03-07122-3/home.html
https://www.ams.org/proc/2004-132-03/S0002-9939-03-07122-3/S0002-9939-03-07122-3.pdf
https://dialnet.unirioja.es/servlet/articulo?codigo=810957

Normal factorisation of polynomials and computational issues: Normal factorisation of polynomials and computational issues.

Authors: Karcanias, N. Mitrouli, M.

Source: Computers & Mathematics with Applications. 45:229-245

Subject Terms: numerical examples, Computational Mathematics, algorithm, Computational Theory and Mathematics, Modelling and Simulation, Factorisation, Greatest common divisor, Approximate computations, Polynomials in real and complex fields: factorization, Numerical computation of solutions to single equations, Polynomials, symbolic computation

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Access URL: https://zbmath.org/2017186
https://doi.org/10.1016/s0898-1221(03)80016-0
https://www.sciencedirect.com/science/article/pii/S0898122103800160
https://pergamos.lib.uoa.gr/uoa/dl/object/3065559

Interruptible Exact Sampling in the Passive Case: Interruptible exact sampling in the passive case

Authors: Keith Crank James Allen Fill

Source: Methodology And Computing In Applied Probability. 4:359-376

Subject Terms: Stopping times, optimal stopping problems, gambling theory, Mathematics - Statistics Theory, stopping time, tree distribution, 0102 computer and information sciences, Statistics Theory (math.ST), 01 natural sciences, reversibility, Sampling theory, sample surveys, FOS: Mathematics, 0101 mathematics, passive case, exact sampling, randomized algorithms, Probability (math.PR), Polynomials in real and complex fields: factorization, Markov chain tree theorem, arborescence, Markov chains (discrete-time Markov processes on discrete state spaces), Markov chain Monte Carlo, 60J10, 68U20 (primary), 60G40, 62D05, 12D05 (secondary), polynomial factorization, perfect simulation, interruptibility, Simulation, Mathematics - Probability

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Access URL: http://arxiv.org/abs/math/0202136
https://zbmath.org/1960129
https://doi.org/10.1023/a:1023514501208
https://ui.adsabs.harvard.edu/abs/2002math......2136C/abstract
https://link.springer.com/article/10.1023/A%3A1023514501208
https://www.ams.jhu.edu/~fill/papers/passive.pdf

On the Malgrange condition for complex polynomials of two variables

Authors: Patrick J. Rabier

Source: manuscripta mathematica. 109:493-509

Subject Terms: asymptotic critical values, Jacobian conjecture, Germs of analytic sets, local parametrization, Malgrange condition, 0211 other engineering and technologies, Polynomials in real and complex fields: factorization, 02 engineering and technology, Jacobian problem, 0101 mathematics, 01 natural sciences, Fibrations, degenerations in algebraic geometry

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Access URL: https://link.springer.com/article/10.1007%2Fs00229-002-0322-8
https://link.springer.com/content/pdf/10.1007/s00229-002-0322-8.pdf
https://link.springer.com/10.1007/s00229-002-0322-8

horner s rule for interval evaluation revisited: Horner's rule for interval evaluation revisited

Authors: Ceberio, Martine C. Granvilliers, L.

Source: Computing. 69(1):51-81

Subject Terms: General methods in interval analysis, Horner's rule, polynomial expression, Polynomials in real and complex fields: factorization, Elementary functions, overestimation problems, Real polynomials: location of zeros, interval evaluation, range of polynomials, Computation of special functions and constants, construction of tables, symbolic forms, factorization, Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral), factorization scheme, Interval arithmetic, Computer Engineering

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Access URL: https://scholarworks.utep.edu/cs_papers/22/
https://link.springer.com/article/10.1007/s00607-002-1448-y
https://link.springer.com/content/pdf/10.1007/s00607-002-1448-y.pdf
https://digitalcommons.utep.edu/cs_papers/22/
https://dblp.uni-trier.de/db/journals/computing/computing69.html#CeberioG02

A formula for separating small roots of a polynomial

Authors: Tateaki Sasaki Akira Terui

Source: ACM SIGSAM Bulletin. 36:19-23

Subject Terms: Numerical computation of solutions to systems of equations, Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, 0102 computer and information sciences, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: https://dl.acm.org/doi/abs/10.1145/603273.603277
https://dblp.uni-trier.de/db/journals/cca/cca36.html#SasakiT02

Real Factorization of Multivariate Polynomials with Integer Coefficients: Real factorization of multivariate polynomials with integer coefficients

Authors: A. Galligo

Source: Journal of Mathematical Sciences. 108:934-941

Subject Terms: Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, Polynomials, factorization in commutative rings, 0102 computer and information sciences, primality test over \(\mathbb R\), 0101 mathematics, 01 natural sciences, probabilistic

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A:1013580019355
https://link.springer.com/content/pdf/10.1023/A:1013580019355.pdf

real factorization of multivariate polynomials with integer coefficients: Real factorization of multivariate polynomials with integer coefficients

Authors: A. Galligo

Source: Journal of Mathematical Sciences. 108(6):934-941

Subject Terms: Polynomials in real and complex fields: factorization, Computational aspects of field theory and polynomials, Polynomials, factorization in commutative rings, primality test over \(\mathbb R\), probabilistic

File Description: application/xml

Access URL: https://link.springer.com/article/10.1023/A:1013580019355
https://link.springer.com/content/pdf/10.1023/A:1013580019355.pdf

Compositions of Polynomials with Coefficients in a Given Field: Compositions of polynomials with coefficients in a given field

Authors: Alan Horwitz

Source: Journal of Mathematical Analysis and Applications. 267:489-500

Subject Terms: polynomial, 39B12, Applied Mathematics, iterate, Polynomials in real and complex fields: factorization, 0102 computer and information sciences, field, 01 natural sciences, composition, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, 0101 mathematics, composition of polynomials, Analysis

File Description: application/xml

Access URL: http://arxiv.org/abs/math/9807027
https://www.sciencedirect.com/science/article/pii/S0022247X01977789
http://www.personal.psu.edu/faculty/a/l/alh4/real.pdf
https://core.ac.uk/display/82140738

Factoring multivariate polynomials via partial differential equations

Authors: GaoShuhong

Source: Mathematics of Computation. 72:801-822

Subject Terms: Hilbert irreducibility theorem, polynomial factorization, absolute irreducibility, partial differential equations, Computational aspects of field theory and polynomials, Polynomials in real and complex fields: factorization, Polynomials, factorization in commutative rings, 0102 computer and information sciences, 0101 mathematics, Symbolic computation and algebraic computation, 01 natural sciences, Number-theoretic algorithms, complexity

File Description: application/xml

Access URL: https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01428-X/S0025-5718-02-01428-X.pdf
https://zbmath.org/1871618
https://doi.org/10.1090/s0025-5718-02-01428-x
http://ui.adsabs.harvard.edu/abs/2003MaCom..72..801G/abstract
https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01428-X/
https://www.ams.org/mcom/2003-72-242/S0025-5718-02-01428-X/S0025-5718-02-01428-X.pdf
https://dblp.uni-trier.de/db/journals/moc/moc72.html#Gao03
https://doi.org/10.1090/S0025-5718-02-01428-X
https://dl.acm.org/doi/10.5555/763377.763392

Another topological proof of the Fundamental Theorem of Algebra: Another topological proof of the fundamental theorem of algebra

Authors: N. Del Toro M. Jimenez Jose Maria Almira

Source: Elemente der Mathematik. 57:32-37

Subject Terms: Polynomials in real and complex fields: factorization, 0101 mathematics, 01 natural sciences

File Description: application/xml

Access URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=57&iss=1&rank=5
https://zbmath.org/1807975
https://doi.org/10.1007/pl00000557
https://link.springer.com/content/pdf/10.1007%2FPL00000557.pdf
https://www.ems-ph.org/doi/10.1007/PL00000557
https://link.springer.com/article/10.1007%2FPL00000557
https://www.ems-ph.org/journals/show_pdf.php?issn=0013-6018&vol=57&iss=1&rank=5

On the irreducibility of the generalized Laguerre polynomials

Authors: T. Y. Lam Michael Filaseta

Source: Acta Arithmetica. 105:177-182

Subject Terms: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), irreducibility, polynomial, generalized Laguerre polynomial, Polynomials in real and complex fields: factorization, 0101 mathematics, 01 natural sciences, Polynomials in number theory, Polynomials (irreducibility, etc.)

File Description: application/xml

Access URL: https://www.impan.pl/shop/publication/transaction/download/product/82947?download.pdf
https://zbmath.org/1860399
https://doi.org/10.4064/aa105-2-4
https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/acta-arithmetica/all/105/2/82947/on-the-irreducibility-of-the-generalized-laguerre-polynomials
http://ui.adsabs.harvard.edu/abs/2002AcAri.105..177F/abstract
http://journals.impan.pl/cgi-bin/doi?aa105-2-4
http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-doi-10_4064-aa105-2-4