GENERAL ORDER MULTIVARIATE PADÉ APPROXIMANTS FOR PSEUDO-MULTIVARIATE FUNCTIONS. II (2009)
Ping Zhou, Annie Cuyt, Jieqing Tan
Abstract. Explicit formulas for general order multivariate Padé approximants of pseudo-multivariate functions are constructed on specific index sets. Examples include the multivariate forms of the...
Computer Algebra Style (Multiprecision) Interval and Complex Arithmetic (2008)
Franky Backeljauw, Annie Cuyt, Brigitte Verdonk, Johan Vervloet
Using the approach in [2, 4, 5], interval bounds for values in R or R∪[−∞, +∞], which is what one is interested in in most industrial applications, can be computed. These approaches, however,...
ICNAAM-2004 0 0–4 Inverting a multidimensional shape from moments (2008)
Annie Cuyt, Gene Golub, Peyman Milanfar, Brigitte Verdonk
The problem of reconstructing a function and/or its domain given its moments is encountered in many areas. Several applications from diverse areas such as probability and statistics [4], signal...
MULTIDIMENSIONAL INTEGRAL INVERSION, WITH APPLICATIONS IN SHAPE RECONSTRUCTION ∗ (2008)
Annie Cuyt, Gene Golub, Peyman Milanfar, Brigitte Verdonk
Abstract. In shape reconstruction, the celebrated Fourier slice theorem plays an essential role. It allows one to reconstruct the shape of a quite general object from the knowledge of its Radon...
08021 Summary -- Numerical Validation in Current Hardware Architectures (2008)
Cuyt, Annie, Krämer, Walter, Luther, Wolfram, Markstein, Peter
Numerical validation in current hardware architectures - From embedded system to high-end computational grids Topics List of participants Schedule List of talks
08021 Abstracts Collection -- Numerical Validation in Current Hardware Architectures (2008)
Luther, Wolfram, Cuyt, Annie, Krämer, Walter, Markstein, Peter
From 06.01. to 11.01.2008, the Dagstuhl Seminar 08021 ``Numerical Validation in Current Hardware Architectures'' was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl....
EXTENDING THE QD-ALGORITHM TO TACKLE MULTIVARIATE PROBLEMS (2007)
Abstract. A lot has been said and done about the qd-algorithm [13, 9, 7, 5, 14]. Our main interest is to analyze how the original algorithm and its various improvements can be generalized for use in...
The course "Computer Arithmetic and Numerical Techniques (2007)
scientific computing course for students with a major in computer science or a combined major mathematics /computer science. But it could as well be taught to any exact or applied science student...
Properties Of Multivariate Homogeneous Orthogonal Polynomials (2007)
Brahim Benouahmane, Annie Cuyt
It is well-known that the denominators of Pad'e approximants can be considered as orthogonal polynomials with respect to a linear functional. This is usually shown by defining Pad'e-type...
On the Froissart phenomenon in multivariate homogeneous Padé approximation (2007)
In univariate Pade approximation we learn from the Froissart phenomenon that Pade approximants to perturbed Taylor series expansions of rational functions exhibit almost cancelling polezero...
A Belgian view of Computational Science and Engineering (2007)
s is typically a one- or two-year program in a field that is in some sense related to, but different from, the discipline chosen by the student in the first two cycles. Hence the third cycle is, in...
A Note on Rational Interpolation (2007)
Introduction Graduate and research students starting in rational approximation theory are soon confronted with different approaches to deal with a particular rational approximation problem. The aim...
Brigitte Verdonk, Annie Cuyt, Dennis Verschaeren
A precision and range independent tool for testing
On the convergence of multivariate Padé approximants (2007)
While the concept of Padé approximant is essentially several centuries old, its multivariate version dates only from the early seventies. In the last century many univariate convergence results were...
Annie Cuyt, Brigitte Verdonk, Dennis Verschaeren
ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission...
Annie Cuyt, Peter Kuterna, Brigitte Verdonk, Dennis Verschaeren
Underflow is a floating-point phenomenon. Although the use of gradual underflow as defended in [2] and [5] is now widespread, most numerical analysts may not be aware of the fact that several...
A precision and range independent tool for testing floating-point arithmetic II: Conversions (1999)
Annie Cuyt, Brigitte Verdonk, Dennis Verschaeren
ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission...
Floating-point versus Symbolic computations in the QD-algorithm (1997)
> n+2 : : : c n+m . . . . . . c n+m\Gamma1 c n+m : : : c n+2m\Gamma2 fi fi fi fi fi fi fi fi fi with H (n) 0 = 1. The series (1) is termed k-normal if H (n) m 6= 0 for m = 0; 1; : : : ; k and n 0....
Kronecker type theorems, normality and continuity of the multivariate Pad e operator (1996)
Annie Cuyt, Kathy Driver, Doron Lubinsky
For univariate functions the Kronecker theorem, stating the equivalence between the existence of an innite block in the table of Pade approximants and the approximated function f being rational, is...
Evaluation of Branched Continued Fractions using Block-Tridiagonal Linear Systems (1988)
The convergent of an ordinary continued fraction can be computed by solving a tridiagonal linear system for its first unknown. In this paper, this approach is generalized to branched continued...
Exploring multivariate Padé approximants for multiple hypergeometric series
Annie Cuyt, Kathy Driver, Jieqing Tan, Brigitte Verdonk
We investigate the approximation of some hypergeometric functions of two variables, namely the Appell functions F i , i = 1; : : : ; 4, by multivariate Pad'e approximants. Section 1 reviews the...