Pokusiński, Bartłomiej; Kamiński, Marcin Numerical convergence and error analysis for the truncated iterative generalized stochastic perturbation-based Finite element method. (English) Zbl 07737572 Comput. Methods Appl. Mech. Eng. 410, Article ID 115993, 39 p. (2023). MSC: 74-XX 65-XX PDFBibTeX XMLCite \textit{B. Pokusiński} and \textit{M. Kamiński}, Comput. Methods Appl. Mech. Eng. 410, Article ID 115993, 39 p. (2023; Zbl 07737572) Full Text: DOI
Bourne, Martin; Winkler, Joab R.; Su, Yi The computation of the greatest common divisor of three bivariate Bernstein polynomials defined in a rectangular domain. (English) Zbl 1472.65021 Appl. Numer. Math. 166, 348-368 (2021). MSC: 65D15 PDFBibTeX XMLCite \textit{M. Bourne} et al., Appl. Numer. Math. 166, 348--368 (2021; Zbl 1472.65021) Full Text: DOI
Pérez-Díaz, Sonia; Shen, Li-Yong Inversion, degree, reparametrization and implicitization of improperly parametrized planar curves using \(\mu \)-basis. (English) Zbl 1465.14056 Comput. Aided Geom. Des. 84, Article ID 101957, 14 p. (2021). Reviewer: Franz Winkler (Linz) MSC: 14Q05 65D18 68U07 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} and \textit{L.-Y. Shen}, Comput. Aided Geom. Des. 84, Article ID 101957, 14 p. (2021; Zbl 1465.14056) Full Text: DOI
Moir, Robert H. C.; Corless, Robert M.; Jeffrey, David J. An unwinding number pair for continuous expressions of integrals. (English) Zbl 1481.30025 J. Symb. Comput. 105, 97-117 (2021). MSC: 30E20 65D30 68W30 PDFBibTeX XMLCite \textit{R. H. C. Moir} et al., J. Symb. Comput. 105, 97--117 (2021; Zbl 1481.30025) Full Text: DOI
Bourne, Martin; Winkler, Joab R.; Su, Yi An approximate factorisation of three bivariate Bernstein basis polynomials defined in a triangular domain. (English) Zbl 1503.65037 J. Comput. Appl. Math. 390, Article ID 113381, 19 p. (2021). MSC: 65D17 41A10 PDFBibTeX XMLCite \textit{M. Bourne} et al., J. Comput. Appl. Math. 390, Article ID 113381, 19 p. (2021; Zbl 1503.65037) Full Text: DOI Link
van der Hoeven, Joris; Lecerf, Grégoire Directed evaluation. (English) Zbl 1475.65013 J. Complexity 60, Article ID 101498, 45 p. (2020). MSC: 65D99 11Y16 12-08 68W30 PDFBibTeX XMLCite \textit{J. van der Hoeven} and \textit{G. Lecerf}, J. Complexity 60, Article ID 101498, 45 p. (2020; Zbl 1475.65013) Full Text: DOI HAL
Bourne, Martin; Winkler, Joab R.; Su, Yi The computation of the degree of the greatest common divisor of three Bernstein basis polynomials. (English) Zbl 1442.13090 J. Comput. Appl. Math. 373, Article ID 112373, 15 p. (2020). MSC: 13P15 33C45 65F99 65H14 PDFBibTeX XMLCite \textit{M. Bourne} et al., J. Comput. Appl. Math. 373, Article ID 112373, 15 p. (2020; Zbl 1442.13090) Full Text: DOI Link
Giesbrecht, Mark; Haraldson, Joseph; Kaltofen, Erich Computing approximate greatest common right divisors of differential polynomials. (English) Zbl 1522.13037 Found. Comput. Math. 20, No. 2, 331-366 (2020). Reviewer: Salah Najib (Khouribga) MSC: 13N10 12-08 13P05 49M15 65L99 PDFBibTeX XMLCite \textit{M. Giesbrecht} et al., Found. Comput. Math. 20, No. 2, 331--366 (2020; Zbl 1522.13037) Full Text: DOI arXiv
Bourne, Martin; Winkler, Joab; Su, Yi The computation of multiple roots of a Bernstein basis polynomial. (English) Zbl 1431.65064 SIAM J. Sci. Comput. 42, No. 1, A452-A476 (2020). MSC: 65H04 12-08 PDFBibTeX XMLCite \textit{M. Bourne} et al., SIAM J. Sci. Comput. 42, No. 1, A452--A476 (2020; Zbl 1431.65064) Full Text: DOI
Emiris, Ioannis Z.; Konaxis, Christos; Laroche, Clément Implicit representations of high-codimension varieties. (English) Zbl 1442.65016 Comput. Aided Geom. Des. 74, Article ID 101764, 19 p. (2019). Reviewer: Rob Corless (London) MSC: 65D17 PDFBibTeX XMLCite \textit{I. Z. Emiris} et al., Comput. Aided Geom. Des. 74, Article ID 101764, 19 p. (2019; Zbl 1442.65016) Full Text: DOI Link
Shen, Li-Yong; Pérez-Díaz, Sonia Numerical polynomial reparametrization of rational curves. (English) Zbl 1473.14112 Comput. Aided Geom. Des. 71, 90-104 (2019). Reviewer: Juan Rafael Sendra (Alcalá de Henares) MSC: 14Q05 65D18 PDFBibTeX XMLCite \textit{L.-Y. Shen} and \textit{S. Pérez-Díaz}, Comput. Aided Geom. Des. 71, 90--104 (2019; Zbl 1473.14112) Full Text: DOI Link
Fazzi, Antonio; Guglielmi, Nicola; Markovsky, Ivan An ODE-based method for computing the approximate greatest common divisor of polynomials. (English) Zbl 1433.65076 Numer. Algorithms 81, No. 2, 719-740 (2019). MSC: 65F45 15A24 65K10 11R09 PDFBibTeX XMLCite \textit{A. Fazzi} et al., Numer. Algorithms 81, No. 2, 719--740 (2019; Zbl 1433.65076) Full Text: DOI Link
Chan, Eunice Y. S.; Corless, Robert M.; Gonzalez-Vega, Laureano; Sendra, J. Rafael; Sendra, Juana Algebraic linearizations of matrix polynomials. (English) Zbl 1433.15018 Linear Algebra Appl. 563, 373-399 (2019). Reviewer: Edgar Pereira (Natal) MSC: 15A22 15A21 65F60 PDFBibTeX XMLCite \textit{E. Y. S. Chan} et al., Linear Algebra Appl. 563, 373--399 (2019; Zbl 1433.15018) Full Text: DOI arXiv
Li, Zijia; Schicho, Josef; Schröcker, Hans-Peter Kempe’s universality theorem for rational space curves. (English) Zbl 1430.70006 Found. Comput. Math. 18, No. 2, 509-536 (2018). MSC: 70B05 14H50 65D17 68U07 PDFBibTeX XMLCite \textit{Z. Li} et al., Found. Comput. Math. 18, No. 2, 509--536 (2018; Zbl 1430.70006) Full Text: DOI arXiv
Beckermann, Bernhard; Labahn, George; Matos, Ana C. On rational functions without Froissart doublets. (English) Zbl 1390.41016 Numer. Math. 138, No. 3, 615-633 (2018). Reviewer: Francisco Pérez Acosta (La Laguna) MSC: 41A21 65F22 PDFBibTeX XMLCite \textit{B. Beckermann} et al., Numer. Math. 138, No. 3, 615--633 (2018; Zbl 1390.41016) Full Text: DOI arXiv
Jia, Xiaohong; Shi, Xiaoran; Chen, Falai Survey on the theory and applications of \(\mu\)-bases for rational curves and surfaces. (English) Zbl 1388.13035 J. Comput. Appl. Math. 329, 2-23 (2018). Reviewer: Carlos Hermoso Ortíz (Madrid) MSC: 13D02 13P10 14Q05 14Q10 65D17 68U05 68U07 PDFBibTeX XMLCite \textit{X. Jia} et al., J. Comput. Appl. Math. 329, 2--23 (2018; Zbl 1388.13035) Full Text: DOI
Guglielmi, Nicola; Markovsky, Ivan An ODE-based method for computing the distance of coprime polynomials to common divisibility. (English) Zbl 1367.65087 SIAM J. Numer. Anal. 55, No. 3, 1456-1482 (2017). MSC: 65K05 90C53 90C30 11A05 PDFBibTeX XMLCite \textit{N. Guglielmi} and \textit{I. Markovsky}, SIAM J. Numer. Anal. 55, No. 3, 1456--1482 (2017; Zbl 1367.65087) Full Text: DOI
Wang, Wei-Guo; Wei, Yimin Mixed and componentwise condition numbers for matrix decompositions. (English) Zbl 1375.65048 Theor. Comput. Sci. 681, 199-216 (2017). MSC: 65F05 15A23 65F35 PDFBibTeX XMLCite \textit{W.-G. Wang} and \textit{Y. Wei}, Theor. Comput. Sci. 681, 199--216 (2017; Zbl 1375.65048) Full Text: DOI
Usevich, Konstantin; Markovsky, Ivan Variable projection methods for approximate (greatest) common divisor computations. (English) Zbl 1375.65062 Theor. Comput. Sci. 681, 176-198 (2017). MSC: 65F30 11A05 11C20 65F20 15B05 65Y20 PDFBibTeX XMLCite \textit{K. Usevich} and \textit{I. Markovsky}, Theor. Comput. Sci. 681, 176--198 (2017; Zbl 1375.65062) Full Text: DOI arXiv
Wu, Wenyuan; Zeng, Zhonggang The numerical factorization of polynomials. (English) Zbl 1454.65031 Found. Comput. Math. 17, No. 1, 259-286 (2017). MSC: 65H04 12-08 13P05 65J20 65F22 PDFBibTeX XMLCite \textit{W. Wu} and \textit{Z. Zeng}, Found. Comput. Math. 17, No. 1, 259--286 (2017; Zbl 1454.65031) Full Text: DOI arXiv
Bourne, Martin; Winkler, Joab R.; Yi, Su The computation of the degree of an approximate greatest common divisor of two Bernstein polynomials. (English) Zbl 1353.65014 Appl. Numer. Math. 111, 17-35 (2017). MSC: 13P15 33C45 65F99 PDFBibTeX XMLCite \textit{M. Bourne} et al., Appl. Numer. Math. 111, 17--35 (2017; Zbl 1353.65014) Full Text: DOI Link
Aprahamian, Mary; Higham, Nicholas J. Matrix inverse trigonometric and inverse hyperbolic functions: theory and algorithms. (English) Zbl 1388.15012 SIAM J. Matrix Anal. Appl. 37, No. 4, 1453-1477 (2016). MSC: 15A24 65F30 65F60 PDFBibTeX XMLCite \textit{M. Aprahamian} and \textit{N. J. Higham}, SIAM J. Matrix Anal. Appl. 37, No. 4, 1453--1477 (2016; Zbl 1388.15012) Full Text: DOI
Petković, Ivan; Neta, Beny On an application of symbolic computation and computer graphics to root-finders: the case of multiple roots of unknown multiplicity. (English) Zbl 1346.65022 J. Comput. Appl. Math. 308, 215-230 (2016). MSC: 65H05 65D18 68W30 PDFBibTeX XMLCite \textit{I. Petković} and \textit{B. Neta}, J. Comput. Appl. Math. 308, 215--230 (2016; Zbl 1346.65022) Full Text: DOI
Schost, Éric; Spaenlehauer, Pierre-Jean A quadratically convergent algorithm for structured low-rank approximation. (English) Zbl 1347.65080 Found. Comput. Math. 16, No. 2, 457-492 (2016). Reviewer: Michael Jung (Dresden) MSC: 65F30 65Y20 15A83 65F10 PDFBibTeX XMLCite \textit{É. Schost} and \textit{P.-J. Spaenlehauer}, Found. Comput. Math. 16, No. 2, 457--492 (2016; Zbl 1347.65080) Full Text: DOI arXiv
Alcázar, Juan Gerardo; Hermoso, Carlos; Muntingh, Georg Symmetry detection of rational space curves from their curvature and torsion. (English) Zbl 1375.65020 Comput. Aided Geom. Des. 33, 51-65 (2015). MSC: 65D17 68T10 14Q05 14H50 PDFBibTeX XMLCite \textit{J. G. Alcázar} et al., Comput. Aided Geom. Des. 33, 51--65 (2015; Zbl 1375.65020) Full Text: DOI arXiv Link
Winkler, Joab R. The Sylvester resultant matrix and image deblurring. (English) Zbl 1360.65078 Boissonnat, Jean-Daniel (ed.) et al., Curves and surfaces. 8th international conference, Paris, France, June 12–18, 2014. Revised selected papers. Cham: Springer (ISBN 978-3-319-22803-7/pbk; 978-3-319-22804-4/ebook). Lecture Notes in Computer Science 9213, 461-490 (2015). MSC: 65D18 PDFBibTeX XMLCite \textit{J. R. Winkler}, Lect. Notes Comput. Sci. 9213, 461--490 (2015; Zbl 1360.65078) Full Text: DOI Link
Feng, Yong; Wu, Wenyuan; Zhang, Jingzhong; Chen, Jingwei Exact bivariate polynomial factorization over \(\mathbb Q\) by approximation of roots. (English) Zbl 1328.65108 J. Syst. Sci. Complex. 28, No. 1, 243-260 (2015). MSC: 65H04 PDFBibTeX XMLCite \textit{Y. Feng} et al., J. Syst. Sci. Complex. 28, No. 1, 243--260 (2015; Zbl 1328.65108) Full Text: DOI
Beckermann, Bernhard; Matos, Ana C. Algebraic properties of robust Padé approximants. (English) Zbl 1311.41009 J. Approx. Theory 190, 91-115 (2015). Reviewer: Marcel G. de Bruin (Haarlem) MSC: 41A21 65F22 PDFBibTeX XMLCite \textit{B. Beckermann} and \textit{A. C. Matos}, J. Approx. Theory 190, 91--115 (2015; Zbl 1311.41009) Full Text: DOI arXiv
Ruatta, Olivier; Sciabica, Mark; Szanto, Agnes Overdetermined Weierstrass iteration and the nearest consistent system. (English) Zbl 1310.65044 Theor. Comput. Sci. 562, 346-364 (2015). MSC: 65F20 13P15 PDFBibTeX XMLCite \textit{O. Ruatta} et al., Theor. Comput. Sci. 562, 346--364 (2015; Zbl 1310.65044) Full Text: DOI arXiv
Shen, Li-Yong; Pérez-Díaz, Sonia Numerical proper reparametrization of parametric plane curves. (English) Zbl 1302.65049 J. Comput. Appl. Math. 277, 138-161 (2015). MSC: 65D17 PDFBibTeX XMLCite \textit{L.-Y. Shen} and \textit{S. Pérez-Díaz}, J. Comput. Appl. Math. 277, 138--161 (2015; Zbl 1302.65049) Full Text: DOI arXiv
Hauenstein, Jonathan D.; Sottile, Frank Newton polytopes and witness sets. (English) Zbl 1304.14077 Math. Comput. Sci. 8, No. 2, 235-251 (2014). Reviewer: Anargyros Katsabekis (Lamia) MSC: 14Q15 65H10 PDFBibTeX XMLCite \textit{J. D. Hauenstein} and \textit{F. Sottile}, Math. Comput. Sci. 8, No. 2, 235--251 (2014; Zbl 1304.14077) Full Text: DOI arXiv
Li, Zhe; Liu, Qi A heuristic verification of the degree of the approximate GCD of two univariate polynomials. (English) Zbl 1302.68333 Numer. Algorithms 67, No. 2, 319-334 (2014). MSC: 68W30 65H04 13P05 11A05 PDFBibTeX XMLCite \textit{Z. Li} and \textit{Q. Liu}, Numer. Algorithms 67, No. 2, 319--334 (2014; Zbl 1302.68333) Full Text: DOI
Barrowclough, Oliver J. D. A basis for the implicit representation of planar rational cubic Bézier curves. (English) Zbl 1293.65024 Comput. Aided Geom. Des. 31, No. 3-4, 148-167 (2014). MSC: 65D17 PDFBibTeX XMLCite \textit{O. J. D. Barrowclough}, Comput. Aided Geom. Des. 31, No. 3--4, 148--167 (2014; Zbl 1293.65024) Full Text: DOI arXiv
Batselier, Kim; Dreesen, Philippe; De Moor, Bart A fast recursive orthogonalization scheme for the Macaulay matrix. (English) Zbl 1293.65064 J. Comput. Appl. Math. 267, 20-32 (2014). MSC: 65F25 65F50 15A18 PDFBibTeX XMLCite \textit{K. Batselier} et al., J. Comput. Appl. Math. 267, 20--32 (2014; Zbl 1293.65064) Full Text: DOI
Christou, D.; Karcanias, N.; Mitrouli, M. Matrix representation of the shifting operation and numerical properties of the ERES method for computing the greatest common divisor of sets of many polynomials. (English) Zbl 1293.12007 J. Comput. Appl. Math. 260, 54-67 (2014). MSC: 12Y05 13P05 65H99 68W30 PDFBibTeX XMLCite \textit{D. Christou} et al., J. Comput. Appl. Math. 260, 54--67 (2014; Zbl 1293.12007) Full Text: DOI
Belhaj, Skander Computing the polynomial remainder sequence via Bézout matrices. (English) Zbl 1285.65022 J. Comput. Appl. Math. 250, 244-255 (2013). MSC: 65F30 PDFBibTeX XMLCite \textit{S. Belhaj}, J. Comput. Appl. Math. 250, 244--255 (2013; Zbl 1285.65022) Full Text: DOI
Fassino, Claudia; Torrente, Maria-Laura Simple varieties for limited precision points. (English) Zbl 1291.65081 Theor. Comput. Sci. 479, 174-186 (2013). MSC: 65D99 68W30 13P15 26C10 PDFBibTeX XMLCite \textit{C. Fassino} and \textit{M.-L. Torrente}, Theor. Comput. Sci. 479, 174--186 (2013; Zbl 1291.65081) Full Text: DOI arXiv
Terui, Akira GPGCD: an iterative method for calculating approximate GCD of univariate polynomials. (English) Zbl 1291.65162 Theor. Comput. Sci. 479, 127-149 (2013). MSC: 65H10 12Y05 12E05 68W30 PDFBibTeX XMLCite \textit{A. Terui}, Theor. Comput. Sci. 479, 127--149 (2013; Zbl 1291.65162) Full Text: DOI arXiv
Corless, Robert M. Pseudospectra of exponential matrix polynomials. (English) Zbl 1291.15020 Theor. Comput. Sci. 479, 70-80 (2013). MSC: 15A18 15A54 65F15 65F60 PDFBibTeX XMLCite \textit{R. M. Corless}, Theor. Comput. Sci. 479, 70--80 (2013; Zbl 1291.15020) Full Text: DOI
Lichtblau, Daniel Approximate Gröbner bases, overdetermined polynomial systems, and approximate GCDs. (English) Zbl 1285.13036 ISRN Comput. Math. 2013, Article ID 352806, 12 p. (2013). Reviewer: Amir Hashemi (Isfahan) MSC: 13P10 65Y04 PDFBibTeX XMLCite \textit{D. Lichtblau}, ISRN Comput. Math. 2013, Article ID 352806, 12 p. (2013; Zbl 1285.13036) Full Text: DOI
Batselier, Kim; Dreesen, Philippe; De Moor, Bart A geometrical approach to finding multivariate approximate LCMs and GCDs. (English) Zbl 1337.65033 Linear Algebra Appl. 438, No. 9, 3618-3628 (2013). MSC: 65F20 15A42 65F35 65F50 PDFBibTeX XMLCite \textit{K. Batselier} et al., Linear Algebra Appl. 438, No. 9, 3618--3628 (2013; Zbl 1337.65033) Full Text: DOI
Winkler, Joab R.; Hasan, Madina; Lao, Xin Two methods for the calculation of the degree of an approximate greatest common divisor of two inexact polynomials. (English) Zbl 1261.12001 Calcolo 49, No. 4, 241-267 (2012). MSC: 12D10 12Y05 65F99 PDFBibTeX XMLCite \textit{J. R. Winkler} et al., Calcolo 49, No. 4, 241--267 (2012; Zbl 1261.12001) Full Text: DOI
Winkler, Joab R.; Lao, Xin; Hasan, Madina The computation of multiple roots of a polynomial. (English) Zbl 1243.65050 J. Comput. Appl. Math. 236, No. 14, 3478-3497 (2012). MSC: 65H04 12Y05 26C10 PDFBibTeX XMLCite \textit{J. R. Winkler} et al., J. Comput. Appl. Math. 236, No. 14, 3478--3497 (2012; Zbl 1243.65050) Full Text: DOI
Barrowclough, Oliver J. D.; Dokken, Tor Approximate implicitization using linear algebra. (English) Zbl 1235.65018 J. Appl. Math. 2012, Article ID 293746, 25 p. (2012). MSC: 65D17 14Q05 14Q10 15-04 PDFBibTeX XMLCite \textit{O. J. D. Barrowclough} and \textit{T. Dokken}, J. Appl. Math. 2012, Article ID 293746, 25 p. (2012; Zbl 1235.65018) Full Text: DOI arXiv
Feng, Yong; Qin, Xiaolin; Zhang, Jingzhong; Yuan, Xun Obtaining exact interpolation multivariate polynomial by approximation. (English) Zbl 1259.65012 J. Syst. Sci. Complex. 24, No. 4, 803-815 (2011). MSC: 65D05 41A05 68W30 PDFBibTeX XMLCite \textit{Y. Feng} et al., J. Syst. Sci. Complex. 24, No. 4, 803--815 (2011; Zbl 1259.65012) Full Text: DOI arXiv
Christou, Dimitrios; Karcanias, Nicos; Mitrouli, Marilena; Triantafyllou, Dimitrios Numerical and symbolical methods for the GCD of several polynomials. (English) Zbl 1255.65062 Van Dooren, Paul (ed.) et al., Numerical linear algebra in signals, systems and control. Selected papers based on the presentations at the international workshop, Kharagpur, India, January 9–11, 2007. In honor of Prof. Biswa Nath Datta. New York, NY: Springer (ISBN 978-94-007-0601-9/hbk; 978-94-007-0602-6/ebook). Lecture Notes in Electrical Engineering 80, 123-144 (2011). MSC: 65D20 12Y05 13P05 PDFBibTeX XMLCite \textit{D. Christou} et al., Lect. Notes Electr. Eng. 80, 123--144 (2011; Zbl 1255.65062) Full Text: DOI Link
Pan, Victor Y.; Zheng, Ai-Long Root-finding by expansion with independent constraints. (English) Zbl 1232.65074 Comput. Math. Appl. 62, No. 8, 3164-3182 (2011). MSC: 65H05 PDFBibTeX XMLCite \textit{V. Y. Pan} and \textit{A.-L. Zheng}, Comput. Math. Appl. 62, No. 8, 3164--3182 (2011; Zbl 1232.65074) Full Text: DOI
Nagasaka, Kosaku Approximate polynomial GCD over integers. (English) Zbl 1248.11104 J. Symb. Comput. 46, No. 12, 1306-1317 (2011). MSC: 11Y16 68W20 65D99 11C08 PDFBibTeX XMLCite \textit{K. Nagasaka}, J. Symb. Comput. 46, No. 12, 1306--1317 (2011; Zbl 1248.11104) Full Text: DOI
Chèze, Guillaume; Galligo, André; Mourrain, Bernard; Yakoubsohn, Jean-Claude A subdivision method for computing nearest gcd with certification. (English) Zbl 1221.68297 Theor. Comput. Sci. 412, No. 35, 4493-4503 (2011). MSC: 68W30 12E05 65Y20 PDFBibTeX XMLCite \textit{G. Chèze} et al., Theor. Comput. Sci. 412, No. 35, 4493--4503 (2011; Zbl 1221.68297) Full Text: DOI
Pan, Victor Y.; Zheng, Ai-Long New progress in real and complex polynomial root-finding. (English) Zbl 1217.65087 Comput. Math. Appl. 61, No. 5, 1305-1334 (2011). MSC: 65H04 PDFBibTeX XMLCite \textit{V. Y. Pan} and \textit{A.-L. Zheng}, Comput. Math. Appl. 61, No. 5, 1305--1334 (2011; Zbl 1217.65087) Full Text: DOI
Galligo, André; Poteaux, Adrien Computing monodromy via continuation methods on random Riemann surfaces. (English) Zbl 1208.14056 Theor. Comput. Sci. 412, No. 16, 1492-1507 (2011). MSC: 14Q05 68W30 13P05 65P99 PDFBibTeX XMLCite \textit{A. Galligo} and \textit{A. Poteaux}, Theor. Comput. Sci. 412, No. 16, 1492--1507 (2011; Zbl 1208.14056) Full Text: DOI Link
Winkler, Joab R.; Lao, Xin The calculation of the degree of an approximate greatest common divisor of two polynomials. (English) Zbl 1246.65062 J. Comput. Appl. Math. 235, No. 6, 1587-1603 (2011). MSC: 65F15 12Y05 26C05 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{X. Lao}, J. Comput. Appl. Math. 235, No. 6, 1587--1603 (2011; Zbl 1246.65062) Full Text: DOI
Yang, Huaiping; Jüttler, Bert; Gonzalez-Vega, Laureano An evolution-based approach for approximate parameterization of implicitly defined curves by polynomial parametric spline curves. (English) Zbl 1229.65045 Math. Comput. Sci. 4, No. 4, 463-479 (2010). MSC: 65D17 65D07 PDFBibTeX XMLCite \textit{H. Yang} et al., Math. Comput. Sci. 4, No. 4, 463--479 (2010; Zbl 1229.65045) Full Text: DOI
Pérez-Díaz, Sonia; Sendra, J. Rafael; Rueda, Sonia L.; Sendra, Juana Approximate parametrization of plane algebraic curves by linear systems of curves. (English) Zbl 1225.65024 Comput. Aided Geom. Des. 27, No. 2, 212-231 (2010). Reviewer: Manuel Gräf (Chemnitz) MSC: 65D17 14Q05 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} et al., Comput. Aided Geom. Des. 27, No. 2, 212--231 (2010; Zbl 1225.65024) Full Text: DOI arXiv Link
Triantafyllou, Dimitrios; Mitrouli, Marilena On rank and null space computation of the generalized Sylvester matrix. (English) Zbl 1198.65082 Numer. Algorithms 54, No. 3, 297-324 (2010). Reviewer: Daniel Kressner (Berlin) MSC: 65F30 15B05 65F05 68W30 15A03 PDFBibTeX XMLCite \textit{D. Triantafyllou} and \textit{M. Mitrouli}, Numer. Algorithms 54, No. 3, 297--324 (2010; Zbl 1198.65082) Full Text: DOI
Terui, Akira GPGCD, an iterative method for calculating approximate GCD, for multiple univariate polynomials. (English) Zbl 1290.68139 Gerdt, Vladimir P. (ed.) et al., Computer algebra in scientific computing. 12th international workshop, CASC 2010, Tsakhkadzor, Armenia, September 6–12, 2010. Proceedings. Berlin: Springer (ISBN 978-3-642-15273-3/pbk). Lecture Notes in Computer Science 6244, 238-249 (2010). MSC: 68W30 12E05 12Y05 65D99 PDFBibTeX XMLCite \textit{A. Terui}, Lect. Notes Comput. Sci. 6244, 238--249 (2010; Zbl 1290.68139) Full Text: DOI arXiv
Winkler, Joab R.; Hasan, Madina A non-linear structure preserving matrix method for the low rank approximation of the Sylvester resultant matrix. (English) Zbl 1196.65083 J. Comput. Appl. Math. 234, No. 12, 3226-3242 (2010). MSC: 65F30 15A24 15A60 12E05 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{M. Hasan}, J. Comput. Appl. Math. 234, No. 12, 3226--3242 (2010; Zbl 1196.65083) Full Text: DOI
Majid, Zanariah Abdul; Suleiman, Mohamed Bin Implementation of parallel three-point block codes for solving large systems of ordinary differential equations. (English) Zbl 1191.65087 Int. J. Comput. Math. 87, No. 6, 1415-1429 (2010). MSC: 65L05 65L06 34A34 65Y05 PDFBibTeX XMLCite \textit{Z. A. Majid} and \textit{M. B. Suleiman}, Int. J. Comput. Math. 87, No. 6, 1415--1429 (2010; Zbl 1191.65087) Full Text: DOI Link
Christou, D.; Karcanias, N.; Mitrouli, M. The ERES method for computing the approximate GCD of several polynomials. (English) Zbl 1185.12005 Appl. Numer. Math. 60, No. 1-2, 94-114 (2010). MSC: 12Y05 65H99 68W30 PDFBibTeX XMLCite \textit{D. Christou} et al., Appl. Numer. Math. 60, No. 1--2, 94--114 (2010; Zbl 1185.12005) Full Text: DOI Link
Kaltofen, Erich Exact certification in global polynomial optimization via rationalizing sums-of-squares. (English) Zbl 1191.13001 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 219-227 (2009). MSC: 13-02 13P99 12Y05 68W30 65F30 14P99 90C22 PDFBibTeX XMLCite \textit{E. Kaltofen}, in: Approximate commutative algebra. Berlin: Springer. 219--227 (2009; Zbl 1191.13001) Full Text: DOI
Zeng, Zhonggang Regularization and matrix computation in numerical polynomial algebra. (English) Zbl 1191.65036 Robbiano, Lorenzo (ed.) et al., Approximate commutative algebra. Berlin: Springer (ISBN 978-3-211-99313-2/pbk; 978-3-211-99314-9/e-book). Texts and Monographs in Symbolic Computation, 125-162 (2009). MSC: 65F15 68W30 13P15 13P10 PDFBibTeX XMLCite \textit{Z. Zeng}, in: Approximate commutative algebra. Berlin: Springer. 125--162 (2009; Zbl 1191.65036) Full Text: DOI
Giesbrecht, Mark; Labahn, George; Lee, Wen-Shin Symbolic-numeric sparse interpolation of multivariate polynomials. (English) Zbl 1167.65003 J. Symb. Comput. 44, No. 8, 943-959 (2009). Reviewer: Martin D. Buhmann (Gießen) MSC: 65D05 74A05 41A63 68W30 PDFBibTeX XMLCite \textit{M. Giesbrecht} et al., J. Symb. Comput. 44, No. 8, 943--959 (2009; Zbl 1167.65003) Full Text: DOI
Pope, Scott R.; Szanto, Agnes Nearest multivariate system with given root multiplicities. (English) Zbl 1168.65347 J. Symb. Comput. 44, No. 6, 606-625 (2009). MSC: 65H10 13P15 68W30 PDFBibTeX XMLCite \textit{S. R. Pope} and \textit{A. Szanto}, J. Symb. Comput. 44, No. 6, 606--625 (2009; Zbl 1168.65347) Full Text: DOI
Winkler, Joab R.; Allan, John D. Structured total least norm and approximate GCDs of inexact polynomials. (English) Zbl 1136.65049 J. Comput. Appl. Math. 215, No. 1, 1-13 (2008). MSC: 65H05 11A05 11C08 PDFBibTeX XMLCite \textit{J. R. Winkler} and \textit{J. D. Allan}, J. Comput. Appl. Math. 215, No. 1, 1--13 (2008; Zbl 1136.65049) Full Text: DOI
Li, Bingyu; Liu, Zhuojun; Zhi, Lihong A structured rank-revealing method for Sylvester matrix. (English) Zbl 1140.65035 J. Comput. Appl. Math. 213, No. 1, 212-223 (2008). Reviewer: Liu Xinguo (Qingdao) MSC: 65F30 68W30 65Y20 15B57 15A03 PDFBibTeX XMLCite \textit{B. Li} et al., J. Comput. Appl. Math. 213, No. 1, 212--223 (2008; Zbl 1140.65035) Full Text: DOI
Elkadi, Mohamed; Yger, Alain Residue calculus and applications. (English) Zbl 1136.32300 Publ. Res. Inst. Math. Sci. 43, No. 1, 55-73 (2007). MSC: 32A27 68W30 65D17 68U07 PDFBibTeX XMLCite \textit{M. Elkadi} and \textit{A. Yger}, Publ. Res. Inst. Math. Sci. 43, No. 1, 55--73 (2007; Zbl 1136.32300) Full Text: DOI
Zhang, Jingzhong; Feng, Yong Obtaining exact value by approximate computations. (English) Zbl 1202.68494 Sci. China, Ser. A 50, No. 9, 1361-1368 (2007). MSC: 68W30 11A55 11J70 33F10 65D99 PDFBibTeX XMLCite \textit{J. Zhang} and \textit{Y. Feng}, Sci. China, Ser. A 50, No. 9, 1361--1368 (2007; Zbl 1202.68494) Full Text: DOI arXiv
Majid, Zanariah Abdul; Suleiman, Mohamed Bin Implementation of four-point fully implicit block method for solving ordinary differential equations. (English) Zbl 1114.65080 Appl. Math. Comput. 184, No. 2, 514-522 (2007). MSC: 65L05 34A34 PDFBibTeX XMLCite \textit{Z. A. Majid} and \textit{M. B. Suleiman}, Appl. Math. Comput. 184, No. 2, 514--522 (2007; Zbl 1114.65080) Full Text: DOI Link
Karcanias, N.; Fatouros, S.; Mitrouli, M.; Halikias, G. H. Approximate greatest common divisor of many polynomials, generalised resultants, and strength of approximation. (English) Zbl 1134.65334 Comput. Math. Appl. 51, No. 12, 1817-1830 (2006). MSC: 65D20 12Y05 13P05 PDFBibTeX XMLCite \textit{N. Karcanias} et al., Comput. Math. Appl. 51, No. 12, 1817--1830 (2006; Zbl 1134.65334) Full Text: DOI
Szilágyi, Ibolya; Jüttler, Bert; Schicho, Josef Local parametrization of cubic surfaces. (English) Zbl 1123.14033 J. Symb. Comput. 41, No. 1, 30-48 (2006). MSC: 14Q10 65D17 PDFBibTeX XMLCite \textit{I. Szilágyi} et al., J. Symb. Comput. 41, No. 1, 30--48 (2006; Zbl 1123.14033) Full Text: DOI
Sun, Yongli; Yu, Jianping Implicitization of parametric curves via Lagrange interpolation. (English) Zbl 1118.14063 Computing 77, No. 4, 379-386 (2006). MSC: 14Q05 68U07 65D05 65D17 PDFBibTeX XMLCite \textit{Y. Sun} and \textit{J. Yu}, Computing 77, No. 4, 379--386 (2006; Zbl 1118.14063) Full Text: DOI
Pérez-Díaz, Sonia; Sendra, Juana; Sendra, J. Rafael Distance bounds of \(\varepsilon\)-points on hypersurfaces. (English) Zbl 1099.68137 Theor. Comput. Sci. 359, No. 1-3, 344-368 (2006). MSC: 68W30 68W25 14Q10 65D18 68U05 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} et al., Theor. Comput. Sci. 359, No. 1--3, 344--368 (2006; Zbl 1099.68137) Full Text: DOI
Soh, Célestin Wafo Nonperturbative semi-analytical source-type solutions of thin-film equation. (English) Zbl 1090.65122 Appl. Math. Comput. 174, No. 2, 1576-1585 (2006). MSC: 65M70 35K30 PDFBibTeX XMLCite \textit{C. W. Soh}, Appl. Math. Comput. 174, No. 2, 1576--1585 (2006; Zbl 1090.65122) Full Text: DOI
Diaz-Toca, Gema M.; Gonzalez-Vega, Laureano Computing greatest common divisors and squarefree decompositions through matrix methods: the parametric and approximate cases. (English) Zbl 1084.65037 Linear Algebra Appl. 412, No. 2-3, 222-246 (2006). Reviewer: C. M. da Fonseca (Coimbra) MSC: 65F30 15A18 65F35 11A05 PDFBibTeX XMLCite \textit{G. M. Diaz-Toca} and \textit{L. Gonzalez-Vega}, Linear Algebra Appl. 412, No. 2--3, 222--246 (2006; Zbl 1084.65037) Full Text: DOI
Schicho, Josef; Szilágyi, Ibolya Numerical stability of surface implicitization. (English) Zbl 1124.65017 J. Symb. Comput. 40, No. 6, 1291-1301 (2005). MSC: 65D17 PDFBibTeX XMLCite \textit{J. Schicho} and \textit{I. Szilágyi}, J. Symb. Comput. 40, No. 6, 1291--1301 (2005; Zbl 1124.65017) Full Text: DOI
Wang, Dongming A simple method for implicitizing rational curves and surfaces. (English) Zbl 1137.65322 J. Symb. Comput. 38, No. 1, 899-914 (2004). MSC: 65D17 14Q10 68W30 PDFBibTeX XMLCite \textit{D. Wang}, J. Symb. Comput. 38, No. 1, 899--914 (2005; Zbl 1137.65322) Full Text: DOI
Pérez-Díaz, Sonia; Sendra, Juana; Sendra, J. Rafael Parametrization of approximate algebraic surfaces by lines. (English) Zbl 1087.65013 Comput. Aided Geom. Des. 22, No. 2, 147-181 (2005). Reviewer: Ivana Linkeová (Praha) MSC: 65D17 14Q10 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} et al., Comput. Aided Geom. Des. 22, No. 2, 147--181 (2005; Zbl 1087.65013) Full Text: DOI
Pan, V. Y. The amended DSeSC power method for polynomial root-finding. (English) Zbl 1077.65049 Comput. Math. Appl. 49, No. 9-10, 1515-1524 (2005). MSC: 65H05 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{V. Y. Pan}, Comput. Math. Appl. 49, No. 9--10, 1515--1524 (2005; Zbl 1077.65049) Full Text: DOI
Zeng, Zhonggang Computing multiple roots of inexact polynomials. (English) Zbl 1079.12007 Math. Comput. 74, No. 250, 869-903 (2005). MSC: 12Y05 65H05 PDFBibTeX XMLCite \textit{Z. Zeng}, Math. Comput. 74, No. 250, 869--903 (2005; Zbl 1079.12007) Full Text: DOI
Homeier, H. H. H. On Newton-type methods with cubic convergence. (English) Zbl 1063.65037 J. Comput. Appl. Math. 176, No. 2, 425-432 (2005). MSC: 65H05 PDFBibTeX XMLCite \textit{H. H. H. Homeier}, J. Comput. Appl. Math. 176, No. 2, 425--432 (2005; Zbl 1063.65037) Full Text: DOI
Feil, T. M.; Homeier, H. H. H. Programs for the approximation of real and imaginary single- and multi-valued functions by means of Hermite-Padé-approximants. (English) Zbl 1196.65043 Comput. Phys. Commun. 158, No. 2, 124-135 (2004). MSC: 65D20 41-04 PDFBibTeX XMLCite \textit{T. M. Feil} and \textit{H. H. H. Homeier}, Comput. Phys. Commun. 158, No. 2, 124--135 (2004; Zbl 1196.65043) Full Text: DOI
Liska, Richard; Shashkov, Mikhail; Ganzha, Victor Analysis and optimization of inner products for mimetic finite difference methods on a triangular grid. (English) Zbl 1058.65115 Math. Comput. Simul. 67, No. 1-2, 55-66 (2004). MSC: 65N06 35J05 65N50 PDFBibTeX XMLCite \textit{R. Liska} et al., Math. Comput. Simul. 67, No. 1--2, 55--66 (2004; Zbl 1058.65115) Full Text: DOI
Homeier, H. H. H. A modified Newton method with cubic convergence: the multivariate case. (English) Zbl 1059.65044 J. Comput. Appl. Math. 169, No. 1, 161-169 (2004). Reviewer: B. Döring (Düsseldorf) MSC: 65H10 PDFBibTeX XMLCite \textit{H. H. H. Homeier}, J. Comput. Appl. Math. 169, No. 1, 161--169 (2004; Zbl 1059.65044) Full Text: DOI
Basilio, J. C.; Moreira, M. V. A robust solution of the generalized polynomial Bézout identity. (English) Zbl 1056.65038 Linear Algebra Appl. 385, 287-303 (2004). Reviewer: Raffaella Pavani (Milano) MSC: 65F30 65F20 15A54 PDFBibTeX XMLCite \textit{J. C. Basilio} and \textit{M. V. Moreira}, Linear Algebra Appl. 385, 287--303 (2004; Zbl 1056.65038) Full Text: DOI
Sommese, Andrew J.; Verschelde, Jan; Wampler, Charles W. Numerical factorization of multivariate complex polynomials. (English) Zbl 1147.13302 Theor. Comput. Sci. 315, No. 2-3, 651-669 (2004). MSC: 13P05 14Q99 65H10 68W30 PDFBibTeX XMLCite \textit{A. J. Sommese} et al., Theor. Comput. Sci. 315, No. 2--3, 651--669 (2004; Zbl 1147.13302) Full Text: DOI
Pérez-Díaz, Sonia; Sendra, Juana; Sendra, J. Rafael Parametrization of approximate algebraic curves by lines. (English) Zbl 1085.68187 Theor. Comput. Sci. 315, No. 2-3, 627-650 (2004). MSC: 68W30 14Q05 65D18 PDFBibTeX XMLCite \textit{S. Pérez-Díaz} et al., Theor. Comput. Sci. 315, No. 2--3, 627--650 (2004; Zbl 1085.68187) Full Text: DOI
Bini, D. A.; Gemignani, L. Bernstein-Bézoutian matrices. (English) Zbl 1071.65014 Theor. Comput. Sci. 315, No. 2-3, 319-333 (2004). Reviewer: Daniela Kacsó (Duisburg) MSC: 65D17 PDFBibTeX XMLCite \textit{D. A. Bini} and \textit{L. Gemignani}, Theor. Comput. Sci. 315, No. 2--3, 319--333 (2004; Zbl 1071.65014) Full Text: DOI
Roanes-Lozano, E.; Roanes-Macías, E.; Villar-Mena, M. A bridge between dynamic geometry and computer algebra. (English) Zbl 1073.68899 Math. Comput. Modelling 37, No. 9-10, 1005-1028 (2003). MSC: 68W30 65D18 68T15 PDFBibTeX XMLCite \textit{E. Roanes-Lozano} et al., Math. Comput. Modelling 37, No. 9--10, 1005--1028 (2003; Zbl 1073.68899) Full Text: DOI
Jones, J.; Karampetakis, N. P.; Pugh, A. C. Solution of discrete ARMA-representations via MAPLE. (English) Zbl 1028.65151 Appl. Math. Comput. 139, No. 2-3, 437-489 (2003). MSC: 65T60 93C55 68W30 PDFBibTeX XMLCite \textit{J. Jones} et al., Appl. Math. Comput. 139, No. 2--3, 437--489 (2003; Zbl 1028.65151) Full Text: DOI
Mulders, T.; Storjohann, A. On lattice reduction for polynomial matrices. (English) Zbl 1028.65038 J. Symb. Comput. 35, No. 4, 377-401 (2003). Reviewer: Hang Tong Lau (St.Laurent/Quebec) MSC: 65F30 15A21 65F40 15A54 15A06 PDFBibTeX XMLCite \textit{T. Mulders} and \textit{A. Storjohann}, J. Symb. Comput. 35, No. 4, 377--401 (2003; Zbl 1028.65038) Full Text: DOI
Chu, Moody T.; Funderlic, Robert E.; Plemmons, Robert J. Structured low rank approximation. (English) Zbl 1018.65057 Linear Algebra Appl. 366, 157-172 (2003). MSC: 65F30 65K05 90C20 PDFBibTeX XMLCite \textit{M. T. Chu} et al., Linear Algebra Appl. 366, 157--172 (2003; Zbl 1018.65057) Full Text: DOI
Hoffman, J. William; Madden, James J.; Zhang, Hong Pseudozeros of multivariate polynomials. (English) Zbl 1017.65047 Math. Comput. 72, No. 242, 975-1002 (2003). Reviewer: Matthew He (Ft.Lauderdale) MSC: 65H05 14P10 13P05 12Y05 26C10 30C15 PDFBibTeX XMLCite \textit{J. W. Hoffman} et al., Math. Comput. 72, No. 242, 975--1002 (2003; Zbl 1017.65047) Full Text: DOI
El-Mikkawy, Moawwad E. A. On solving linear systems of the Pascal type. (English) Zbl 1023.65019 Appl. Math. Comput. 136, No. 1, 195-202 (2003). MSC: 65F05 65Y15 15B36 PDFBibTeX XMLCite \textit{M. E. A. El-Mikkawy}, Appl. Math. Comput. 136, No. 1, 195--202 (2003; Zbl 1023.65019) Full Text: DOI
Christiansen, Søren Derivation and investigation of fifth order quadrature formulas for biharmonic boundary integral operators. (English) Zbl 0977.65109 Appl. Numer. Math. 37, No. 1-2, 145-159 (2001). Reviewer: J.C.F.Telles (Rio de Janeiro) MSC: 65N38 65D32 35J40 65N12 31A30 31A10 PDFBibTeX XMLCite \textit{S. Christiansen}, Appl. Numer. Math. 37, No. 1--2, 145--159 (2001; Zbl 0977.65109) Full Text: DOI
Pegon, Pierre Alternative characterization of time integration schemes. (English) Zbl 0982.70003 Comput. Methods Appl. Mech. Eng. 190, No. 20-21, 2707-2727 (2001). MSC: 70-08 70J35 65L05 PDFBibTeX XMLCite \textit{P. Pegon}, Comput. Methods Appl. Mech. Eng. 190, No. 20--21, 2707--2727 (2001; Zbl 0982.70003) Full Text: DOI
Foupouagnigni, Mama; Hounkonnou, M. Norbert; Ronveaux, André The fourth-order difference equation satisfied by the associated orthogonal polynomials of the \(\Delta\)-Laguerre-Hahn class. (English) Zbl 0948.65140 J. Symb. Comput. 28, No. 6, 801-818 (1999). Reviewer: Costică Moroşanu (Iaşi) MSC: 65Q05 39A10 33C45 PDFBibTeX XMLCite \textit{M. Foupouagnigni} et al., J. Symb. Comput. 28, No. 6, 801--818 (1999; Zbl 0948.65140) Full Text: DOI
Yang, Lu Recent advances on determining the number of real roots of parametric polynomials. (English) Zbl 0957.65041 J. Symb. Comput. 28, No. 1-2, 225-242 (1999). Reviewer: H.Kriete (Göttingen) MSC: 65H05 12Y05 26C10 PDFBibTeX XMLCite \textit{L. Yang}, J. Symb. Comput. 28, No. 1--2, 225--242 (1999; Zbl 0957.65041) Full Text: DOI
Kuijt, Frans; van Damme, Ruud Monotonicity preserving interpolatory subdivision schemes. (English) Zbl 0947.65007 J. Comput. Appl. Math. 101, No. 1-2, 203-229 (1999). Reviewer: J.Illán González (Vigo) MSC: 65D05 65D17 PDFBibTeX XMLCite \textit{F. Kuijt} and \textit{R. van Damme}, J. Comput. Appl. Math. 101, No. 1--2, 203--229 (1999; Zbl 0947.65007) Full Text: DOI
Rupprecht, David An algorithm for computing certified approximate GCD of \(n\) univariate polynomials. (English) Zbl 0964.12007 J. Pure Appl. Algebra 139, No. 1-3, 255-284 (1999). Reviewer: V.Trevisan (Porto Alegre) MSC: 12Y05 65F30 15A18 65Y99 68W30 PDFBibTeX XMLCite \textit{D. Rupprecht}, J. Pure Appl. Algebra 139, No. 1--3, 255--284 (1999; Zbl 0964.12007) Full Text: DOI
Tuzun, Robert E.; Burkhardt, Paul; Secrest, Don Accurate computation of individual and tables of \(3\)-\(j\) and \(6\)-\(j\) symbols. (English) Zbl 0933.65022 Comput. Phys. Commun. 112, No. 2-3, 112-148 (1998). Reviewer: Mariana Gaşpar (Iaşi) MSC: 65D20 33F05 33C80 20H15 81V55 PDFBibTeX XMLCite \textit{R. E. Tuzun} et al., Comput. Phys. Commun. 112, No. 2--3, 112--148 (1998; Zbl 0933.65022) Full Text: DOI