"Numerical and Symbolic algorithms"

Dear Colleagues,

It is well known the increasing attention paid in the
last years to the theory of Orthogonal Polynomials.
In particular since their applications in a lot of different areas
like numerical integration, spectral methods, interpolation,
approximation theory, etc. Also
in combinatorics, mathematical physics, quantum physics, etc. For this reason
the *Universidad Carlos III de Madrid* organizes every two years
an international workshop devoted to this topic. The first edition in 1992 was
dedicated to Sobolev orthogonal polynomials, in 1994 to
polynomials orthogonal in the unit circle, and the last one
IWOP'96 ,
held in 1996, to the applications of orthogonal polynomials in mathematical physics.

The main **aim** of the 1998's edition of the
Workshop was that a reduced number of invited mathematicians discuss and review
recent progress of the Theory of **Orthogonal Polynomials** with
** special emphasis ** in the *numerical applications and simbolic algorithms*.
The Workshop took place
in the main building of the Escuela Politécnica Superior,
(room 2F01, located in the second floor of the building)
Universidad Carlos III de Madrid, ** Leganés** (Madrid).

The topics considered were:

- Combinatorics
- Numerical Linear Algebra
- Quadrature formulas
- Spectral methods in boundary value problems
- Symbolic algorithms and software

**How to get Escuela Politécnica Superior**

The best way to get the Escuela Politécnica Superior is by using the
trains * Cercanias* which can be reach from Atocha Railway Station
* Cercanias* Line C5 (direction Fuenlabrada) and leave the train in the
Station * Leganés* (not in Zarzaquemada!) which is at 5 min. waking fron the
University. Please see a scheme of getting to the
University Campus
, or if you prefer, see a more detailed map

- Walter Gautschi (Purdue University, USA)
- Gene Golub (Stanford University, USA)
- Wolfram Koepf (Hochschule für Technik, Wirtschaft und Kultur Leipzig, Germany)
- Yvon Maday (Université Pierre et Marie Curie, France)
- Marko Petkovsek (University of Ljubljana, Slovenia)
- Doron Zeilberger (Temple University, USA)

The Organizing Committee was:

- M. Alfaro (Univ. de Zaragoza),
- R. Álvarez-Nodarse (Secretary) (Univ. Carlos III, Univ de Sevilla),
- J. Arvesú (Univ. Carlos III),
- F. Marcellán (Chairman) (Univ. Carlos III)

The Scientific Committee was:

- R. Álvarez-Nodarse (Univ. Carlos III, Univ de Sevilla),
- J. S. Dehesa (Univ. de Granada),
- E. Godoy (Univ. Vigo),
- G.López Lagomasino (Univ. Carlos III),
- F. Marcellán (Univ. Carlos III)
- R. Yáñez (Univ. de Granada) and
- A. Zarzo (Univ. Politénica de Madrid)

The Proceedings of the Workshop have been appeared
as a special issue of * Electronic Transactions on Numerical
Analysis* (ETNA) (see the URL site
http://etna.mcs.kent.edu/)

On Monday, June 29, at 9:00 was be the registration and the Openning session.

(*) On Wednesday, July 1, at 13:30 took place a symbolic-software presentation by Addlink Software Científico.

Time | Monday | Tuesday | Wednesday | Thursday | |
---|---|---|---|---|---|

9:30 | Koepf | Koepf | Golub | Golub | |

10:30 | Gautschi | Gautschi | Zeilberger | Zeilberger | |

11:30 | Break | Break | Break | Break | |

12:00 | Calvetti | Yáñez | Alvarez | Lagomasino | |

12:30 | Perea | Yakhlef | García | Pasquini (*) | |

13:00 | Salam | P. López | Fernández | Lorente | |

13:30 | Lunch | Lunch | Lunch(**) | Lunch | |

16:00 | Petkovsek | Petkovsek | Maday | Maday | |

17:00 | Reichel | Mastroianni | González-Vera | Ruano | |

17:30 | Break | Break | Break | Break | |

17.45 | Milovanovic | Medem | Bello | Gil | |

18:15 | Fuchs | Ricci | Kravanja | Segura | |

18:45 | Cala | Costa | Lewanowicz | Bogatirev |

** Titles**

- Walter Gautschi,
*Orthogonal Polynomials and Quadrature*and*Rational Gauss-type Quadrature Rules* - Gene Golub,
*Bounds for the Entries of Matrix Functions with Applications to Preconditioning*and*Inverting Shape From Moments* - Wolfram Koepf,
*Software for the Algorithmic Work with Orthogonal Polynomials and Special Functions* - Yvon Maday,
*The Basic spectral element and mortar element methods for elliptic problems*and*The spectral element methods for resolution of the Stokes and Navier-Stokes problems* - Marko Petkovsek,
*Linear Operators and Compatible Polynomial Bases* - Doron Zeilberger,
*The Unreasonable Power of Orthogonal Polynomials in Combinatorics I and II*

** Titles**

- María Alvarez de Morales
*Non-standard orthogonality for Meixner polynomials* - Manuel Bello
*Zero distribution of orthogonal polynomials with respect to varying measures on the unit circle* - Andrei B. Bogatyrev
*On construction of polynomials least deviating from zero on a system of segments* - Francisco Cala Rodríguez
*Quadrature Formulas for Rational Functions* - Daniela Calvetti
*Estimation of the L-curve via Lanczos bidiagonalization* - Cecilia Costa
*Quaternion Block Tridiagonal System* - María Victoria Fernández-Muñoz
*Bernstein--Sobolev operators* - Erich Fuchs
*Algorithms to compute polynomials orthogonal with respect to non-standard discrete inner products* - Esther García Caballero
*Sobolev orthogonal polynomials: Interpolation and Approximation* - Amparo Gil
*A Numerical Algorithm for Parabolic Cylinder Functions* - Pablo González-Vera
*Product Integration Rules on the Unit Circle* - Peter Kravanja
*On locating clusters of zeros of analytic functions* - Stanislaw Lewanowicz
*Recurrence relations for the coefficients of the Fourier series expansions with respect to the classical orthogonal polynomials* - Guillermo López Lagomasino
*Approximation of Transfer Functions of Infinite-Dimensional Dynamical Systems by Rational Functions with Prescribed Poles* - Pedro López
*Riesz's theorem and the Nevanlinna parametrization for Orthogonal Matrix Polynomials* - Miguel Lorente
*Creation and annihilation operators for orthogonal polynomials of discrete and continuous variables* - Giuseppe Mastroianni
*Numerical evaluation of integral transforms on the real line with singular or weakly singular kernels* - Juan C. Medem
*On semiclasical polynomials: A singular distributional equation* - Gradimir Milovanovic
*Generalized Quadratures and Muntz Polynomials* - Lionello Pasquini
*``Priori" Estimates of Eigenvalues Conditioning by Spectral Portraits* - Carmen Perea
*Some results on nonnegative splittings of second type* - Lothar Reichel
*Computation of Gauss-Kronrod quadrature rules* - Paolo E. Ricci
*An iterative method for computing the eigenvalues of second kind Fredholm operators and applications* - Jorge Ruano
*Algebraic properties of hypergeometric-type functions. A computer algebra approach* - Ahmed Salam
*A new generalization of Lanczos type methods related to the vector orthogonal polynomials* - Javier Segura
*Evaluation of Associated Legendre Functions Off the Cut* - Hossain O. Yakhlef
*On Orthogonal Matrix Polynomials* - Rafael J. Yáñez
*Connection coefficients for discrete hypergeometric type polynomials on uniform and non-uniform lattices*

Click here to see the abstracts of the invited lectures. The abstracts of the short communications will be included in the Book of Abstracts. The abstracts are also available in postscript format

Click here to see the participants.

To get more information please contact with:

** R. Álvarez-Nodarse (*)**
and ** F. Marcellán (**) **

Maintained by Renato Álvarez-Nodarse: E-Mail: ran@us.es