Alphonse P. Magnus

From a photograph full photo (jpg file 61K) showing me between Walter Van Assche (left) and Ken McLaughlin (right). Photography taken in front of the library of exact sciences in Louvain-la-Neuve on 13th May 1996 by Therese McLaughlin. Obrigado!

In front of the Muslim castle of Cassis (France). Picture by Diego Dominici, July 2007.

Institut Math. Univ. Louvain Chemin du Cyclotron 2 B-1348 Louvain-la-Neuve Belgium Tel ++32 10 473157 Fax ++32 10 472530 mail to alphonse.magnus@uclouvain.be

(From Altdorfer's "The battle of Alexander at Issus") web museum 1 .. web mus. 2 .. web mus. 3 ..

(Thanks to Bruno Vroman) The full, much more explicit picture ..

Former lectures

Remez algorithm in java

Remez algorithm in javascript

Matière vue en 2009 (pdf) (déc. 2009)
Matière vue en 2010 (pdf) (déc. 2010)

Equations aux dérivées partielles 2

Matière vue 2008-2009(pdf) (mai 2009)
Matière vue 2009-2010(pdf) (mai 2010)
 

Diffusion des euros

nouveaux développements (mars 2003)

Programme du cours MAFY 1181. Actualités des mathématiques et de la physique. Année académique 2008-2009.
27 mars. Approximations de fonctions. Archéologie des tables de logarithmes.

Analyse numérique 3

1. 1997: CF-Hankel-BMO(A) Rational approximation. 216K
2. 1997: more of above, 120K
3. 1997: still more ("1/9"), 68K
4. MAPA3011A 1997-98 New difference calculus. 500K
5. MAPA3xxxA 1998-99 Padé approx. branch points. 526K
6.   1999-2000: Semi-classical orthogonal polynomials on the unit circle.
   Abstract: Semi-classical orthogonal polynomials on the unit circle are examined. Special care is given to generalized Jacobi polynomials.
   MAPA3072A 1999-2000 Semi-classical orth. pol. on unit circle. pdf (1999-2000, 2002-2003, 2012-2013)
   
7.   2000-2002: Abstract: several ways to build rational approximations to various species of analytic functions are examined. Special emphasis is put on strong asymptotic estimates of the form $ f(z) -R_n(z) \sim \sigma(z) \rho^n(z)$, when such estimates are available, and on approximation to exponentials of polynomials.
   MAPA3071 2000-2002 Complex approximation and interpolation. ps-gz 183K (as of 11 Oct. 2001)
   MAPA3071 2000-2002 Complex approximation and interpolation. pdf 521K (as of 11 Oct. 2001)

2000-2001: Abstract: several ways to build rational approximations to various species of analytic functions are examined. Special emphasis is put on strong asymptotic estimates of the form $ f(z) -R_n(z) \sim \sigma(z) \rho^n(z)$, when such estimates are available.
1st lecture: Friday 13 October 2000, room b101-102 as above, 14h30-16h.
2001-2002: Abstract: several ways to build rational approximations to various species of analytic functions are examined. Special emphasis is put on approximation to exponentials of polynomials.
1st lecture: Friday 12 October 2001, room b101-102 as above, 14h30-16h.
ps and pdf files (Oct. 2001):
pdf file (521K)
gzipped ps file (183K)
March 2002): a summary (19 pages)  pdf file (240K)     ps file (349K)
The slides (5 pages)    pdf file (121K)     ps file (216K)

2002-2003: Abstract: Generalized Jacobi orthogonal polynomials on the unit circle are examined: differential equations, recurrence relations, asymptotic properties.
1st lecture: Friday 11 October 2002, room b101-102 as above, 14h30-16h.
pdf file Mar. 2003 (408K)
(March 2003): bits and pieces of a solution of Grünbaum-Delsarte-Janssen-Vries problem in m3xxx99.pdf

2006-2007. MAPA3071. Elliptic lattices. (pdf 640K)

  Colloque OPSFA "Orthogonal polynomials, Special functions and Applications" 2 au 6 juillet 2007  http://www.cirm.univ-mrs.fr/liste_rencontre/Rencontres2007/Valent07/Valent07.html
Rational interpolation to solutions of Riccati difference equations on elliptic lattices. The slides (pdf)     The pre-preprint (pdf) The preprint of Nov. 2008 (pdf)

Rational interpolation to exponential-like functions on elliptic lattices, 3èmes Journées Approximation May 15-16, 2008 Salle de Réunion, Bâtiment M2 Laboratoire Paul Painlevé UMR 8524 Université de Lille 1, FRANCE
The slides (pdf)     The pre-preprint (pdf)

Workshop: "Elliptic integrable systems, isomonodromy problems, and hypergeometric functions". Yu.I. Manin, M. Noumi, E.M. Rains, H. Rosengren, V.P. Spiridonov (organizers) Hausdorff Center for Mathematics, Bonn 21-25 July, 2008 http://www.hausdorff-center.uni-bonn.de/elliptic-integrable-systems

Elliptic difference equations. The elliptic logarithm. The slides (pdf)      http://www.emis.de/journals/SIGMA/Elliptic-Integrable-Systems.html
The preprint of Nov 2008. (pdf)
Alphonse P. Magnus, Elliptic Hypergeometric Solutions to Elliptic Difference Equations, SIGMA 5 (March 2009), 038, 12 pages , http://www.emis.de/journals/SIGMA/2009/038/sigma09-038.pdf

OPSFA-10 (Orthogonal Polynomials, Special Functions and Applications), Leuven 2009 http://wis.kuleuven.be/OPSFA/OPSFA10.html

Rational Freud equations, my slides Freud2009s.pdf

Approximation Days 2012 2-3 July, 2012, Leuven, Belgium http://wis.kuleuven.be/events/ad12
Threepieces2012s.pdf
The Polignac problem has been solved long ago, it is in Whittaker & Watsons's book! see PolWhit.pdf
More on gen. Jacobi pol. asymptotics on unit circle in Semi-classical orth. pol. on unit circle. pdf (1999-2000, 2002-2003, 2012-2013)

The Journal

Papers

Alphonse P. Magnus, Elliptic Hypergeometric Solutions to Elliptic Difference Equations, SIGMA 5 (March 2009), 038, 12 pages , http://www.emis.de/journals/SIGMA/2009/038/sigma09-038.pdf

Alphonse P. Magnus, Viviane Pierrard, Formulas for recurrence coefficients of orthogonal polynomials related to Lorentzian-like weights, Journal of Computational and Applied Mathematics, Volume 219, Issue 2, Pages 431-440 (1 October 2008) , Special Issue dedicated to Prof. Claude Brezinski, on the occasion of his retirement from the University of Sciences and Technologies of Lille in June 2006, Edited by M. Prévost, M. Redivo-Zaglia and F. Wielonsky .
The pdf preprint, with the % in the acknowledgements!

Germain, M.; Magnus, A.; Steenberghe, V., How to design and use the clean development mechanism under the Kyoto Protocol? A developing country perspective, Environmental and Resource Economics , Volume 38, Number 1, September 2007, pp. 13-30.

M.Germain, A.Magnus: Prices versus quantities: stock pollution control with repeated choice of the instrument, J. Comp. Appl. Math. . 197 (2006) 437-445 the pdf (145K) preprint, Oct. 2005.

A.P. Magnus, " Freud equations for Legendre polynomials on a circular arc and solution of the Grünbaum-Delsarte-Janssen-Vries problem" , Journal of Approximation Theory, Volume 139, Issues 1-2, This Volume is Dedicated to Barry Simon on the Occasion of his Sixtieth Birthday, March-April 2006, Pages 75-90. Keywords: Unit circle orthogonal polynomials
The pdf (200K) preprint, May 2005.

A.P. Magnus, J. Meinguet, The elliptic functions and integrals of the `1/9' problem, presented at Antwerpen international conference on rational approximation June 6--11 1999 ICRA99, Numerical Algorithms 24: (1-2) (2000) 117-139. See more here.

M. Germain, A.P. Magnus, Progrès technique et durée de vie du capital, IRES Discussion Paper 9911 (March 1999) http://www.ires.ucl.ac.be/DP/Biblio_html/9911.html
 
In preparation: V.Pierrard and A.P.Magnus: Lorentzian orthogonal polynomials
The FORTRAN77 program

All about the "1/9" constant!

Software: Freud machine

NEW (2012) Bar-le-Duc stuff BarlD.htm

NEW (June 2003): pre-preprint Freud equations for Legendre polynomials on a circular arc and solution of the Gr\"unbaum-Delsarte-Janssen-Vries problem.
The pdf file
The java program

Other addresses

Other math. stuff
math. textbooks online
Some homepages
Various addresses.
info HTML.