Alphonse P. Magnus
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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!
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In front of the Muslim castle of Cassis (France). Picture by
Diego Dominici, July 2007.
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" Vêtu de probité candide et cousu de fil blanc "
" Bold, math, and italic! "
Best wishes deux mil 24, pdf file
(2023,
(2022,
2021,2020,2019,2018,2017,2016,2015,2014,2013,2012, 2011, 2010, 2009, 2008, 2007, 2006, 2005, 2004, 2003)
CV (html)
Pascal Maroni 1933-2024 Maroni2024.pdf Much more in opsfnl312.pdf
André Ronveaux 1932-2023.
It is my sad duty to report the passing of André Ronveaux, professor of
mathematical physics in Montréal (Canada) and Namur (Belgium). He wrote
many papers, most on orthogonal polynomials, books and proceedings, such as
' Heun’s Differential Equations', . Oxford U. P., 1995, Bar-le-Duc meeting
proceedings, Springer lect. notes math. vol. 1171, 1985, and lesser known books
on lectures, such as 'Équations aux différences finies et équations différentielles pour tous.
Expérience pilote d'enseignement au Québec (1965-1969)',
Lidec, Montréal, 1966, 1968, and Univ. Montréal 1969, 2nd printing:
presses universitaires de Namur 2017, a healthy reaction against the 'new math'
rage of the period.
André was a competent scientist, a devoted teacher, and a benevolent human being.
Alphonse Magnus.
Much more in OPSF 31.1, in
opsfnl311.pdf
2023
Chasing special biorthogonal rational functions, poster presented at
"Integrable Systems, Random Matrices and Special Functions at UBI 20 November, 2023
University of Beira Interior, Covilhã, Portugal"
https://asimoe1.wixsite.com/workshop
The poster (pdf) The slides (pdf)
First comments, April 2024.
Satoshi Tsujimoto, Luc Vinet and Alexei Zhedanov already gave a full description of the Hahn case in "An algebraic description of the bispectrality of the biorthogonal rational functions of Hahn type", Proceedings of the American Mathematical Society, 149 (November 2020), pp.715-728..
The same authors also expanded the Masson's constructions in "The rational Heun operator and Wilson biorthogonal functions", The Ramanujan Journal, (May 2021), https://doi.org/10.1007/s11139-020-00383-7 (23pp).
"An extended scheme of classical special functions" by Vyacheslav P. Spiridonov tells the last word on elliptic hypergeometric
expansions of biorthogonal rational functions, up to 12V11 expansions (amazing!), to appear in a future book in honor of R. Askey (G. Andrews et al., eds; Springer,
2024 or 2025), arXiv:2403.16264v1 [math.CA] 24 Mar 2024.
Jean Meinguet, 1930-2023 We are very sorry to report the passing away of Jean Meinguet,
professor of numerical analysis and numerical computer science at the
université catholique de Louvain (Leuven, Louvain-la-Neuve, Belgium).
He graduated in engineering (1954), went to Zurich to learn numerical
analysis with H. Rutishauser and E. Stiefel, worked in the "Comité
d'étude et d'exploitation des calculateurs électroniques (Belgian
Science Foundation, Brussels, Belgium)" on programming a Bell
Telephone co. computer, got a phd on filtering problems, advised by
Vitold Belevitch (1960).
He organized, and taught, numerical analysis, numerical functional
analsis, numerical algorithmics, numerical linear algebra (with
emphasis on the theory of determinants), algol 60 and other
languages. He published results on an amazing scope of subjects:
rounding error analysis, such as stability of Cholesky factorization,
multivariate spline interpolation, optimal recovery, rational
interpolation (the Cauchy problem), Adamjan-Arov-Krein-Takagi theory,
extremal measures determination. The most often heard, and most
exact, statement on him is: "He knows everything".
Alphonse Magnus, Paul Van Dooren, Yves Genin
NA Digest Wednesday, November 01, 2023 Volume 23 : Issue 23
202?:
A. P. Magnus, J. Meinguet, Strong asymptotics of best rational approximation to the exponential function on a bounded interval,
to appear in Mat.Sb. https://www.mathnet.ru/eng/sm8815
Key words: rational approximation, exponential function, complex potential
2010 Mathematics Subject Classification:
30E10 Approximation in the complex domain
30E15 Asymptotic representations in the complex domain
31A15 Potentials and capacity, harmonic measure, extremal length
33E05 Elliptic functions and integrals
33F05 Numerical approximation and evaluation
41A20 Approximation by rational functions
%41A21 Padé approximation
41A25 Rate of convergence, degree of approximation
41A80 Remainders in approximation formulas
Abstract. We apply recent findings of complex approximation theory
to best rational approximation of degree n to
the exponential of -(n+n)x on [0,c]. The error norm behaves like
the nth power of the main approximation rate times the n th
power of a secondary approximation rate. The computation of the first rate is a
consequence of works of A.A.Gonchar, E.A. Rakhmanov, and Herbert Stahl
done in the 1980s; the complete asymptotic description has been achieved by
A. Aptekarev in the first years of the 21st century. The solution is
given in terms of elliptic integrals of the three kinds.
The last preprint .
2020:
Alphonse P. Magnus, François Ndayiragije, André Ronveaux, About families of orthogonal polynomials satisfying Heun's differential equation,
Journal of Approximation Theory, 263 (2021) 105522,
https://doi.org/10.1016/j.jat.2020.105522
The last preprint.
Abstract. We consider special families of orthogonal polynomials
satisfying differential equations. Besides known hypergeometric
cases, we look especially for
Heun's differential
equations.We show that such equations are satisfied by orthogonal
polynomials related to some classical weight functions modified
by Dirac weights or by division of powers of binomials.
An appropriate set of biorthogonal rational functions, or 2-point Padé
approximations, is also described.
Keywords: orthogonal polynomials, Padé
approximation, Heun's differential equation.
2010 Mathematics Subject Classification:
34M35, %Differential equations in the complex domain, singularities, monodromy, local behavior of solutions, normal forms,
34M55, %Painlevé and other special equations; classification, hierarchies;
41A21, %Padé approximation
42C05, %Orthogonal functions and polynomials, general theory,
81Q05. % Closed and approximate solutions to the Schr\"odinger eq. etc.
15 Jan. 2019:
Why did we live almost 200 years with the wrong face of Legendre?
BMS-NCM Newsletter #121, January 15, 2019, 11-12.
http://bms.ulb.ac.be/BMSNCM/BMSNE121.pdf
2017:
Alphonse P. Magnus, François Ndayiragije, André Ronveaux:
Heun differential equation satisfied by some classical
biorthogonal rational functions.
Preliminary notes. Poster shown at the
14th International Symposium on Orthogonal Polynomials, Special Functions and Applications
(OPSFA-14), University of Kent, Canterbury, UK, July 3-7, 2017.
The pdf file
April 2015, Aug. 2016, Dec. 2016, Apr. 2017, Nov. 2017, Feb 2018 Gaussian integration formulas for logarithmic
weights and application to 2-dimensional solid-state lattices
Journal of Approximation Theory 228 (2018) 21-57
https://doi.org/10.1016/j.jat.2018.02.001
Key words: Numerical analysis, Integration formulas, Logarithmic singularities,
Solid-state physics, 2-dimensional lattices, Graphene.
2010 Mathematics Subject Classification:
42A16 Fourier coefficients, Fourier series of functions with special properties,
special Fourier series,
42C05 Orthogonal functions and polynomials, general theory,
42C10 Fourier series in special orthogonal functions (Legendre polynomials, etc.),
47B36 Jacobi (tridiagonal) operators (matrices) and generalizations,
65D32 Quadrature and cubature formulas,
81Q05 Closed and approximate solutions to the Schrödinger eq. etc.
Abstract. The making of Gaussian numerical integration formulas is
considered for weight functions with logarithmic singularities.
Chebyshev modified moments are found most convenient here. The
asymptotic behavior of the relevant recurrence coefficients is
stated in two conjectures. The relation with the recursion method in
solid-state physics is summarized, and more details are given for
some two-dimensional lattices (square lattice and hexagonal
(graphene) lattice).
Last preprint grapheneR6.pdf
The 69999 first recurrence coefficients of graphene
graphene69999.txt (2M)
Research lectures:
Postscript & pdf files of lectures
Analyse numerique 3
Special topics in approximation theory.
- 1997: CF-Hankel-BMO(A) Rational approximation. 216K
- 1997: more of above, 120K
- 1997: still more ("1/9"), 68K
- MAPA3011A 1997-98 New difference calculus. 500K
- MAPA3xxxA 1998-99 Padé approx. branch points. 526K
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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)
-
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)
Special
topics in numerical linear algebra 2000
Seminar
series on rational approximation and systems theory 2002
SEMINAR SERIES ON
ITERATIVE METHODS FOR LARGE SCALE PROBLEMS (2005)
A piece of Belgian literature
A piece of computer science (1970)
The Journal
Journal of Approximation Theory at Ohio State.
Journal of Approximation Theory at Technion.
www.academicpress.com/jat
Papers
Alphonse P. Magnus, Rational interpolation to solutions of Riccati difference equations on elliptic lattices, Journal of Computational and Applied Mathematics,
available online: 26-FEB-2009,
http://dx.doi.org/10.1016/j.cam.2009.02.047
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
Papers by A.P.Magnus
see also in my CV
All about the "1/9" constant!
see here
Software: Freud machine
Freud programs and doc
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
Former lectures
Analyse numérique: approximation, interpolation, intégration
pdf A4 (in French) 2200K Sept. 2010
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
pdf (in French) 2300K (Jan 2010)
Matière vue 2008-2009(pdf) (mai 2009)
Matière vue 2009-2010(pdf) (mai 2010)
Diffusion des euros
INMA2375.
Projet intégré MAP 2002-2003.
voir ici le fichier eurodiff.htm
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
Room b101-102 , Math. Dept., Building de Hemptinne,
Chemin du Cyclotron 2 , 1348 Louvain-la-Neuve
Other addresses
Univ Louvain
new Univ Louvain www.uclouvain.be
fac fsa
fac sc
search engines ( KuLeuven)
Libraries Louvain la Neuve
Libraries Belgium
Periodicals (ANTILOPE)
Math. Dept , including math. libraries
Math. Institute
CESAME Institute
IAPV
Current Contents (Local link)
Calcul intensif
Département INMA
Other math. stuff
math. textbooks online
Some homepages
Various addresses.
info HTML.
17 Apr. 2024