Publications

B. Benouahmane, A. Cuyt, and I. Yaman. Near-minimal cubature formulae on the disk. IMA J. Numer. Anal., 39(1):297–314, 2019. (Published online December 08, 2017) [DOI]

A. Cuyt and O. Salazar Celis. Multivariate data fitting with error control. BIT, 59(1):35–55, 2019. (Published online September 17, 2018) [DOI]

A. Cuyt, R. Louw, C. Segers, and D. de Villiers. Rapid design and modelling of wideband sinuous antenna reflector feeds through blended rational interpolation. Int. J. Numer. Model., 32(1):e2458, 2019. [DOI]

Annie Cuyt and Wen-shin Lee. Multivariate exponential analysis from the minimal number of samples. Adv. Comput. Math., 44:987–1002, 2018. (Published online November 16, 2017) [DOI]

A. Cuyt, M.-n. Tsai, M. Verhoye, and W.-s. Lee. Faint and clustered components in exponential analysis. Appl. Math. Comput., 327:93–103, 2018. (toolbox and examples are available)

Gerlind Plonka, Katrin Wannenwetsch, Annie Cuyt, and Wen-shin Lee. Deterministic sparse FFT for m-sparse vectors. Numer. Algorithms, 78(1):133–159, 2018. [DOI]

M. Briani, A. Cuyt, and W.-s. Lee. A hybrid Fourier-Prony method. ArXiv e-print 1706.04520 [math.NA], Universiteit Antwerpen, 2017.

Annie Cuyt and Wen-shin Lee. An analog Chinese Remainder Theorem. Technical report, Universiteit Antwerpen, 2017.

A. Cuyt, S. Peelman, and I. Yaman. How to deal with interpolation points that are not well-spaced. Technical report, Universiteit Antwerpen, 2017.

A. Cuyt, O. Salazar Celis, M. Lukach, and K. In 't Hout. Analytic models for parameter dependency in option price modelling. Numer. Algorithms, 73:15–31, 2016.

Annie Cuyt, Wen-shin Lee, and Xianglan Yang. On tensor decomposition, sparse interpolation and Padé approximation. Jaén J. Approx., 8(1):33–58, 2016.

B.Ali Ibrahimoglu and A. Cuyt. Sharp bounds for Lebesgue constants of barycentric rational interpolation. Exp. Math., 25:347–354, 2016.

Yongliang Zhang, Annie Cuyt, Wen-shin Lee, Giovanni Lo Bianco, Gang Wu, Yu Chen, and David Day-Uei Li. Towards unsupervised fluorescence lifetime imaging using low dimensional variable projection. Opt. Express, 24(23):26777–26791, 2016.

M. Collowald, A. Cuyt, E. Hubert, W.-s. Lee, and O. Salazar Celis. Numerical reconstruction of convex polytopes from directional moments. Adv. Comput. Math., 41(6):1079–1099, 2015. (see the correct version of this paper) [DOI]

Annie Cuyt. Approximation theory. In N. Higham, editor, Princeton Companion to Applied Mathematics, pages 248–262. Princeton University Press, 2015.

Oliver Salazar Celis, Lingzhi Liang, Damiaan Lemmens, Jacques Tempere, and Annie Cuyt. Determining and benchmarking risk neutral distributions implied from option prices. Appl. Math. Comput., 258:372–387, 2015.

F. Backeljauw, S. Becuwe, A. Cuyt, J. Van Deun, and D. Lozier. Validated evaluation of special mathematical functions. Science of Computer Programming, 90:2–20, 2014. [DOI]

A. Cuyt, O. Salazar Celis, and M. Lukach. Multidimensional IIR filters and robust rational interpolation. Multidimens. Syst. Signal Process., 25:447–471, 2014. [DOI]

Oliver Salazar Celis, Annie Cuyt, Dirk Deschrijver, Dries Vande Ginste, and Tom Dhaene. Macromodeling of high-speed interconnects by positive interpolation of vertical segments. Appl. Math. Model., 37:4874–4882, 2013. [DOI]

Annie Cuyt, Irem Yaman, Ali Ibrahimoglu, and Brahim Benouahmane. Radial orthogonality and Lebesgue constants on the disk. Numer. Algorithms, 61:291–313, 2012. [DOI]

Romain Pacanowski, Oliver Salazar Celis, Christophe Schlick, Xavier Granier, Pierre Poulin, and Annie Cuyt. Rational BRDF. IEEE Trans. Vis. Comput. Graphics, 18:1824–1835, 2012. [DOI]

M. Colman, A. Cuyt, and J. Van Deun. Validated computation of certain hypergeometric functions. ACM Trans. Math. Software, 38, 2011. Article nr. 11. [DOI]

Annie Cuyt and Wen-shin Lee. Sparse interpolation of multivariate rational functions. Theoret. Comput. Sci., 412:1445–1456, 2011. [DOI]

A. Cuyt, B. Benouahmane, Hamsapriye, and I. Yaman. Symbolic-numeric Gaussian cubature rules. Appl. Numer. Math., 61:929–945, 2011. [DOI]

H.T. Nguyen, A. Cuyt, and O. Salazar Celis. Comonotone and coconvex rational interpolation and approximation. Numer. Algorithms, 58:1–21, 2011. [DOI]

H. Allouche and A. Cuyt. Reliable root detection with the qd-algorithm: when Bernoulli, Hadamard and Rutishauser cooperate. Appl. Numer. Math., 60:1188–1208, 2010. [DOI]

Annie Cuyt and Xianglan Yang. A practical error formula for multivariate rational interpolation and approximation. Numer. Algorithms, 55:233–243, 2010. [DOI]

R.B. Lenin, A. Cuyt, K. Yoshigoe, and S. Ramaswamy. Computing packet loss probabilities of D-BMAP/PH/1/N queues with group services. Perform. Eval., 67:160–173, 2010. [DOI]

A. Ludu, J. Van Deun, M.V. Milosevic, A. Cuyt, and F. Peeters. Analytic treatment of vortex states in cylindrical superconductors in applied axial magnetic field. J. Math. Phys., 51:082903–1 – 082903–29, 2010. [DOI]

F. Backeljauw and A. Cuyt. Algorithm 895: A continued fractions package for special functions. ACM Trans. Math. Software, 36, 2009. Article nr. 15. [DOI]

Annie Cuyt. Approximation theory. In B.W. Wah, editor, Encyclopedia of Computer Science and Engineering, pages 163–171. John Wiley & Sons, 2009. [DOI]

P. Zhou, A. Cuyt, and J. Tan. General order multivariate Padé approximants for pseudo-multivariate functions II. Math. Comp., 78(268):2137–2155, 2009. [DOI]

Annie Cuyt and Wen-shin Lee. A new algorithm for sparse interpolation of multivariate polynomials. Theoret. Comput. Sci., 409:180–185, 2008. [DOI]

W. Schreppers and A. Cuyt. Algorithm 871: A C/C++ precompiler for the autogeneration of multiprecision programs. ACM Trans. Math. Software, 34(1), 2008. Article nr. 5. [DOI]

J. Abouir and A. Cuyt. Stable multidimensional model reduction and IIR filter design. Int. J. Comput. Sci. Math., 1:16–27, 2007. [DOI]

O. Salazar Celis, A. Cuyt, and B. Verdonk. Rational approximation of vertical segments. Numer. Algorithms, 45:375–388, 2007. [DOI]

S. Becuwe and A. Cuyt. On the fast solution of Toeplitz-block linear systems arising in multivariate approximation theory. Numer. Algorithms, 43:1–24, 2006. [DOI]

S. Becuwe and A. Cuyt. Reliable multiprecision evaluation of special functions. ECMI Newsletter, March-April:16–17, 2006.

A. Cuyt, R.B. Lenin, S. Becuwe, and B. Verdonk. Adaptive multivariate rational data fitting with applications in electromagnetics. IEEE Trans. Microw. Theory Techn., 54:2265–2274, 2006. [DOI]

A. Cuyt, J. Tan, and P. Zhou. General order multivariate Padé approximants for pseudo-multivariate functions. Math. Comp., 75:727–741, 2006. [DOI]

A. Cuyt, B. Verdonk, and H. Waadeland. Efficient and reliable multiprecision implementation of elementary and special functions. SIAM J. Sci. Comput., 28:1437–1462, 2006. [DOI]

F. Backeljauw and A. Cuyt. A constructive criticism of the C/C++ proposal for complex arithmetic. Reliab. Comput., 11:313–319, 2005. [DOI]

P. Borwein, A. Cuyt, and P. Zhou. Explicit construction of general multivariate Padé approximants to an Appell function. Adv. Comput. Math., 22:249–273, 2005. [DOI]

A. Bultheel, A. Cuyt, W. Van Assche, M. Van Barel, and B. Verdonk. Generalizations of orthogonal polynomials. J. Comput. Appl. Math., 179:57–95, 2005. [DOI]

A. Cuyt, G. Golub, P. Milanfar, and B. Verdonk. Multidimensional integral inversion, with applications in shape reconstruction. SIAM J. Sci. Comput., 27:1058–1070, 2005. [DOI]

B. Verdonk, J. Vervloet, and A. Cuyt. Blending set and interval arithmetic for maximal reliability. Computing, 74:41–65, 2005. [DOI]

A. Cuyt, R.B. Lenin, and K. Van der Borght. Sensitivity analysis and fast computation of packet loss probabilities in multiplexer models. Appl. Numer. Anal. Comp. Math., 1:18–35, 2004. [DOI]

A. Cuyt, J. Sijbers, B. Verdonk, and D. Van Dyck. Region and contour identification of physical objects. Appl. Numer. Anal. Comp. Math., 1:343–352, 2004. [DOI]

J. Abouir, A. Cuyt, and R. Orive. Multivariate two-point Padé-type and two-point Padé approximants. Numer. Algorithms, 33:11–26, 2003. [DOI]

A. Cuyt, R.B. Lenin, G. Willems, C. Blondia, and P. Rousseeuw. Computing packet loss probabilities in multiplexer models using rational approximation. IEEE Trans. Comput., 52:633–644, 2003. [DOI]

A. Cuyt, P. Kuterna, B. Verdonk, and D. Verschaeren. Underflow revisited. Calcolo, 39(3):169–179, 2002. [DOI]

B. Benouahmane and A. Cuyt. Properties of multivariate homogeneous orthogonal polynomials. J. Approx. Theory, 113:1–20, 2001. [DOI]

A. Cuyt and R.B. Lenin. Multivariate rational approximants for multi-class closed queueing networks. IEEE Trans. Comput., 50:1279–1288, 2001. [DOI]

A. Cuyt, B. Verdonk, S. Becuwe, and P. Kuterna. A remarkable example of catastrophic cancellation unraveled. Computing, 66:309–320, 2001. [DOI]

B. Verdonk, A. Cuyt, and D. Verschaeren. A precision and range independent tool for testing floating-point arithmetic I: basic operations, square root and remainder. ACM Trans. Math. Software, 27:92–118, 2001. [DOI]

B. Verdonk, A. Cuyt, and D. Verschaeren. A precision and range independent tool for testing floating-point arithmetic II: conversions. ACM Trans. Math. Software, 27:119–140, 2001. [DOI]

B. Benouahmane and A. Cuyt. Multivariate orthogonal polynomials, homogeneous Padé approximants and Gaussian cubature. Numer. Algorithms, 24:1–15, 2000. [DOI]

S. Becuwe and A. Cuyt. On the Froissart phenomenon in multivariate homogeneous Padé approximation. Adv. Comput. Math., 11(1):21–40, 1999. [DOI]

A. Cuyt. How well can the concept of Padé approximant be generalized to the multivariate case?. J. Comput. Appl. Math., 105:25–50, 1999. [DOI]

A. Cuyt, K. Driver, J. Tan, and B. Verdonk. Exploring multivariate Padé approximants for multiple hypergeometric series. Adv. Comput. Math., 10:29–49, 1999. [DOI]

A. Cuyt, K. Driver, J. Tan, and B. Verdonk. A finite sum representation of the Appell series F₁(a,b,b';c;x,y). J. Comput. Appl. Math., 105:213–219, 1999. [DOI]

A. Cuyt. Floating-point versus symbolic computations in the qd-algorithm. J. Symbolic Comput., 24:695–703, 1997. [DOI]

A. Cuyt and D. Lubinsky. A de Montessus theorem for multivariate homogeneous Padé approximants. Ann. Numer. Math., 4:217–228, 1997.

A. Cuyt and B. Verdonk. Computational science and engineering at Belgian universities. IEEE Comput. Science & Engrg., 4(4):79–83, 1997. (see also the extended versions A Belgian view of Computational Science and Engineering and Computer Arithmetic and Numerical Techniques) [DOI]

A. Cuyt and B. Verdonk. A note on univariate rational interpolation. Commun. Anal. Theory Contin. Fract., VI:63–73, 1997.

D. Verschaeren, A. Cuyt, and B. Verdonk. On the need for predictable floating-point arithmetic in the programming languages FORTRAN90 and C/C++. ACM SIGPLAN Notices, 32(3):57–64, 1997. [DOI]

J. Abouir, A. Cuyt, P. González-Vera, and R. Orive. On the convergence of general order multivariate Padé-type approximants. J. Approx. Theory, 86:216–228, 1996. [DOI]

A. Cuyt and D. Lubinsky. On the convergence of multivariate Padé approximants. Bull. Belgian Math. Soc. Suppl. `Numerical Analysis', pages 51–61, 1996.

A. Cuyt, K. Driver, and D. Lubinsky. A direct approach to convergence of multivariate nonhomogeneous Padé approximants. J. Comput. Appl. Math., 69:353–366, 1996. [DOI]

A. Cuyt, K. Driver, and D. Lubinsky. Kronecker type theorems, normality and continuity of the multivariate Padé operator. Numer. Math., 73:311–327, 1996. [DOI]

A. Cuyt, K. Driver, and D. Lubinsky. Nuttall-Pommerenke theorems for homogeneous Padé approximants. J. Comput. Appl. Math., 67:141–146, 1996. [DOI]

A. Cuyt, K. Driver, and D. Lubinsky. On the size of lemniscates of polynomials in one and several variables. Proc. Amer. Math. Soc., 124:2123–2136, 1996. [DOI]

A. Cuyt. Exploring covariance, consistency and convergence in Padé approximation theory. In S.P. Singh, editor, NATO ASI "Approximation theory, Wavelets and Applications" Series C 454, pages 55–86. Kluwer Academic Publisher, 1995. [DOI]

H. Allouche and A. Cuyt. Singular rules for a multivariate quotient-difference algorithm. Numer. Algorithms, 6:137–168, 1994. [DOI]

H. Allouche and A. Cuyt. Well-defined determinant representations for non-normal multivariate rational interpolants. Numer. Algorithms, 6:119–135, 1994. [DOI]

A. Cuyt. On the convergence of the multivariate "homogeneous" qd-algorithm. BIT, 34:535–545, 1994. [DOI]

A. Cuyt, B. Verdonk, and J. Verelst. Intelligent object-oriented scientific computation. Math. Comput. Simulation, 36:401–411, 1994. [DOI]

J. Abouir and A. Cuyt. Multivariate partial Newton-Padé and Newton-Padé type approximants. J. Approx. Theory, 72:301–316, 1993. [DOI]

H. Allouche and A. Cuyt. Unattainable points in multivariate rational interpolation. J. Approx. Theory, 72:159–173, 1993. [DOI]

A. Cuyt and B. Verdonk. The need for knowledge and reliability in numeric computation: case study of multivariate Padé approximation. Acta Appl. Math., 33:273–302, 1993. [DOI]

P. Janssens and A. Cuyt. How does PASCAL-XSC compare to other programming languages with respect to the IEEE standard?. ACM SIGPLAN Notices, 28(8):57–66, 1993. [DOI]

H. Allouche and A. Cuyt. On the structure of a table of multivariate rational interpolants. Constr. Approx., 8:69–86, 1992. [DOI]

A. Cuyt. Extension of "a multivariate convergence theorem of the de Montessus de Ballore type" to multipoles. J. Comput. Appl. Math., 41:323–330, 1992. [DOI]

A. Cuyt. Padé approximation in one and more variables. In S.P. Singh, editor, NATO ASI "Approximation theory, spline functions and applications" Series C vol. 356, pages 41–68. Kluwer Academic Publisher, 1992. [DOI]

A. Cuyt. Rational Hermite interpolation in one and more variables. In S.P. Singh, editor, NATO ASI "Approximation theory, spline functions and applications" Series C vol. 356, pages 69–104. Kluwer Academic Publisher, 1992. [DOI]

A. Cuyt and B. Verdonk. Multivariate rational data fitting: general data structure, maximal accuracy and object orientation. Numer. Algorithms, 3:159–172, 1992. [DOI]

A. Cuyt, S. Ogawa, and B. Verdonk. Model reduction of multidimensional linear shift-invariant recursive systems using Padé techniques. Multidimens. Syst. Signal Process., 3:309–322, 1992. [DOI]

A. Cuyt. A class of adaptive multivariate nonlinear iterative methods. Rocky Mountain J. Math., 21:171–185, 1991. [DOI]

A. Cuyt, W.B. Jones, and B. Verdonk. Model reduction and stability of two-dimensional recursive systems. Rocky Mountain J. Math., 21:187–208, 1991. [DOI]

J. Abouir and A. Cuyt. Error formulas for multivariate rational interpolation and Padé approximation. J. Comput. Appl. Math., 31:233–241, 1990. [DOI]

A. Cuyt. A multivariate convergence theorem of the "de Montessus de Ballore" type. J. Comput. Appl. Math., 32:47–57, 1990. [DOI]

A. Cuyt. Old and new multidimensional convergence accelerators. Appl. Numer. Math., 6(3):169–185, 1990. [DOI]

A. Cuyt. A multivariate qd-like algorithm. BIT, 28:98–112, 1988. [DOI]

A. Cuyt and B. Verdonk. Evaluation of branched continued fractions using block-tridiagonal linear systems. IMA J. Numer. Anal., 8:209–217, 1988. [DOI]

A. Cuyt and B. Verdonk. Multivariate reciprocal differences for branched Thiele continued fraction expansions. J. Comput. Appl. Math., 21:145–160, 1988. [DOI]

A. Cuyt and B. Verdonk. A review of branched continued fraction theory for the construction of multivariate rational approximants. Appl. Numer. Math., 4:263–271, 1988. [DOI]

A. Cuyt, L. Jacobsen, and B. Verdonk. Instability and modification of Thiele interpolating continued fractions. Appl. Numer. Math., 4:253–262, 1988. [DOI]

A. Cuyt. A bibliography of the works of Prof. Dr. H. Werner. J. Comput. Appl. Math., 19:3–8, 1987.

A. Cuyt. The Euler-Minding series for branched continued fractions. J. Comput. Appl. Math., 17:369–373, 1987. [DOI]

A. Cuyt. A recursive computation scheme for multivariate rational interpolants. SIAM J. Numer. Anal., 24:228–239, 1987. [DOI]

A. De Muynck, A. Cuyt, R. Liefooghe, M. Parent, P. Van der Stuyft, and B. Verdonk. A computer aided teaching program in epidemiology and biostatistics. Ann. Soc. belge Méd. trop., 67:79–81, 1987.

A. Cuyt. Multivariate Padé approximants revisited. BIT, 26:71–79, 1986. [DOI]

A. Cuyt. Singular rules for the calculation of non-normal multivariate Padé approximants. J. Comput. Appl. Math., 14:289–301, 1986. [DOI]

A. Cuyt. A Montessus de Ballore theorem for multivariate Padé approximants. J. Approx. Theory, 43:43–52, 1985. [DOI]

A. Cuyt. A review of multivariate Padé approximation theory. J. Comput. Appl. Math., 12-13:221–232, 1985. [DOI]

A. Cuyt and L. Rall. Computational implementation of the multivariate Halley method for solving nonlinear systems of equations. ACM Trans. Math. Software, 11:20–36, 1985. [DOI]

A. Cuyt and P. Van Der Cruyssen. Rounding error analysis for forward continued fraction algorithms. Comput. Math. Appl., 11:541–564, 1985. [DOI]

A. Cuyt and B. Verdonk. Multivariate rational interpolation. Computing, 34:41–61, 1985. [DOI]

A. Cuyt. Operator Padé approximants: some ideas behind the theory and a numerical illustration. In S. Singh and others, editors, NATO ASI "Approximation theory and spline functions" Series C vol. 136, pages 271–288. Reidel, Dordrecht, 1984. [DOI]

A. Cuyt. The qd-algorithm and Padé approximants in operator theory. SIAM J. Math. Anal., 15:746–752, 1984. [DOI]

A. Cuyt and B. Verdonk. General order Newton-Padé approximants for multivariate functions. Numer. Math., 43:293–307, 1984. [DOI]

A. Cuyt, L. Wuytack, and H. Werner. On the continuity of the multivariate Padé operator. J. Comput. Appl. Math., 11:95–102, 1984. [DOI]

A. Cuyt. Accelerating the convergence of a table with multiple entry. Numer. Math., 41:281–286, 1983. [DOI]

A. Cuyt. A comparison of some multivariate Padé approximants. SIAM J. Math. Anal., 14:195–202, 1983. [DOI]

A. Cuyt. The epsilon-algorithm and Padé approximants in operator theory. SIAM J. Math. Anal., 14:1009–1014, 1983. [DOI]

A. Cuyt. Multivariate Padé approximants. J. Math. Anal. Appl., 96:283–293, 1983. [DOI]

A. Cuyt. A projection-property for abstract rational (1-point) approximants. J. Operator Theory, 10:127–131, 1983.

A. Cuyt. The qd-algorithm and multivariate Padé approximants. Numer. Math., 42:259–269, 1983. [DOI]

A. Cuyt and P. Van Der Cruyssen. Abstract Padé approximants for the solution of a system of nonlinear equations. Comput. Math. Appl., 9:617–624, 1983. [DOI]

A. Cuyt. The epsilon-algorithm and multivariate Padé approximants. Numer. Math., 40:39–46, 1982. [DOI]

A. Cuyt. Numerical stability of the Halley-iteration for the solution of a system of nonlinear equations. Math. Comp., 38:171–179, 1982. [DOI]

A. Cuyt. Padé approximants in operator theory for the solution of nonlinear differential and integral equations. Comput. Math. Appl., 8:445–466, 1982. [DOI]

A. Cuyt. Regularity and normality of abstract Padé approximants. Projection property and product property. J. Approx. Theory, 35:1–11, 1982. [DOI]

A. Cuyt. On the properties of abstract rational (1-point) approximants. J. Operator Theory, 6:195–216, 1981.