Research Interests

• Orthogonal rational functions
• Rational quadrature formulas
• Rational Krylov

Publications

1. K. Deckers, A. Mougaida, and H. Belhadjsalah
   Algorithm 973: Extended Rational Fejér Quadrature Rules based on Chebyshev Orthogonal Rational Functions,
   ACM Transactions on Mathematical Software 43(4), Article No. 37, 2017.
2. K. Deckers,
   Christoffel-Darboux-type formulae for orthonormal rational functions with arbitrary complex poles,
   IMA Journal of Numerical Analysis 35(4):1842-1863, 2015.
3. K. Deckers and A. Bultheel,
   Rational interpolation: II. Quadrature and convergence,
   Journal of Mathematical Analysis and Applications 397(1):124-141, 2013.
4. K. Deckers and A. Bultheel,
   Rational interpolation: I. Least square convergence,
   Journal of Mathematical Analysis and Applications 395(2):455-464, 2012.
5. K. Deckers and J.S. Geronimo,
   Baxter's difference systems and orthogonal rational functions,
   Journal of Approximation Theory 164(8):1085-1096, 2012.
6. K. Deckers and D.S. Lubinsky,
   How poles of orthogonal rational functions affect their Christoffel functions,
   Journal of Approximation Theory 164(9):1184-1199, 2012.
7. K. Deckers and D.S. Lubinsky,
   Christoffel functions and universality limits for orthogonal rational functions,
   Analysis and Applications 10(3):271-294, 2012.
8. K. Deckers and A. Bultheel,
   The existence and construction of rational Gauss-type quadrature rules,
   Applied Mathematics and Computation 218(20):10299-10320, 2012.
9. K. Deckers, A. Bultheel, and F. Perdomo-Pío,
   Rational Gauss-Radau and rational Szegö-Lobatto quadrature on the interval and the unit circle respectively,
   Jaen Journal on Approximation 3(1):15-66, 2011.
10. K. Deckers, M.J. Cantero, L. Moral, and L. Velázquez,
    An extension of the associated rational functions on the unit circle,
    Journal of Approximation Theory 163(4):524-546, 2011.
11. K. Deckers, A. Bultheel, and J. Van Deun
    A generalized eigenvalue problem for quasi-orthogonal rational functions,
    Numerische Mathematik 117(3):463-506, 2011.
12. K. Deckers, A. Bultheel, R. Cruz-Barroso, and F. Perdomo-Pío,
    Positive rational interpolatory quadrature formulas on the unit circle and the interval,
    Applied Numerical Mathematics 60(12):1286-1299, 2010.
13. A. Chesnokov, K. Deckers and M. Van Barel,
    A numerical solution of the constrained weighted energy problem,
    Journal of Computational and Applied Mathematics 235(4):950-965, 2010.
14. K. Deckers, J. Van Deun, and A. Bultheel,
    Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm,
    Advances in Engineering Software 40(8):707-717, 2009.
15. K. Deckers and A. Bultheel,
    Orthogonal rational functions with complex poles: The Favard theorem,
    Journal of Mathematical Analysis and Applications 356(2):764-768, 2009.
    
16. K. Deckers and A. Bultheel,
    Orthogonal rational functions and rational modifications of a measure on the unit circle,
    Journal of Approximation Theory 157(1):1-18, 2009.
17. A. Bultheel, R. Cruz-Barroso, K. Deckers, and P. González-Vera,
    Rational Szegö quadratures associated with Chebyshev weight functions,
    Mathematics of Computation 78(266):1031-1059, 2009.
18. K. Deckers and A. Bultheel,
    Recurrence and asymptotics for orthogonal rational functions on an interval,
    IMA Journal of Numerical Analysis 29(1):1-23, 2009.
19. K. Deckers and A. Bultheel,
    Associated rational functions based on a three-term recurrence for orthogonal rational functions,
    IAENG International Journal of Applied Mathematics 38(4):214-222, 2008.
20. J. Van Deun, K. Deckers, A. Bultheel, and J. A. C. Weideman,
    Algorithm 882: Near best fixed pole rational interpolation with applications in spectral methods,
    ACM Transactions on Mathematical Software 35(2):14:1-14:21, 2008.
21. K. Deckers, J. Van Deun, and A. Bultheel,
    Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1],
    Mathematics of Computation 77(262):967-983, 2008.
    
22. K. Deckers, J. Van Deun, and A. Bultheel,
    An extended relation between orthogonal rational functions on the unit circle and the interval [-1,1],
    Journal of Mathematical Analysis and Applications 334(2):1260-1275, 2007.

1. K. Deckers, J. Van Deun, and A. Bultheel,
   Computing rational Gauss-Chebyshev quadrature formulas with complex poles,
   In Proceedings of the Fifth International Conference on Engineering Computational Technology, B. H. V. Topping, G. Montero, and R. Montenegro, Eds. Civil-Comp Press, Stirlingshire, United Kingdom. Paper 30, 2006.
   
2. K. Deckers and A. Bultheel,
   Orthogonal Rational Functions, Associated Rational Functions And Functions Of The Second Kind,
   In Proceedings of the World Congress on Engineering 2008, S. I. Ao, L. Gelman, D. W. L. Hukins, A. Hunter and A. M. Korsunsky, Eds. Newswood Limited, International Association of Engineers, London, United Kingdom. Volume 2 of Lecture Notes in Engineering and Computer Science, pages 838--843, 2008.
   

1. K. Deckers and A. Bultheel,
   Rational interpolation and quadrature on the interval and on the unit circle,
   Report TW 574, Dept. of Computer Science, KU Leuven, 2010.
2. K. Deckers and A. Bultheel,
   The existence and construction of rational Gauss-type quadrature rules,
   Report TW 573, Dept. of Computer Science, KU Leuven, 2010.
3. K. Deckers, A. Bultheel, and J. Van Deun,
   A generalized eigenvalue problem for quasi-orthogonal rational functions,
   Report TW 571, Dept. of Computer Science, KU Leuven, 2010.
4. A. Chesnokov, K. Deckers and M. Van Barel,
   A numerical solution of the constrained weighted energy problem,
   Report TW 540, Dept. of Computer Science, KU Leuven, 2009.
5. K. Deckers and A. Bultheel,
   Orthogonal rational functions with complex poles: The Favard theorem,
   Report TW 518, Dept. of Computer Science, KU Leuven, 2008.
6. K. Deckers and A. Bultheel,
   Orthogonal rational functions, associated rational functions and functions of the second kind,
   Report TW 514, Dept. of Computer Science, KU Leuven, 2008.
7. K. Deckers and A. Bultheel,
   A Favard theorem for rational functions with complex poles,
   Report TW 512, Dept. of Computer Science, KU Leuven, 2008.
8. K. Deckers and A. Bultheel,
   Rational Krylov sequences and orthogonal rational functions,
   Report TW 499, Dept. of Computer Science, KU Leuven, 2007.
9. K. Deckers, J. Van Deun, and A. Bultheel,
   Computing rational Gauss-Chebyshev quadrature formulas with complex poles,
   Report TW 462, Dept. of Computer Science, KU Leuven, 2006.
10. K. Deckers, J. Van Deun, and A. Bultheel,
    Rational Gauss-Chebyshev quadrature formulas for complex poles outside [-1,1],
    Report TW 448, Dept. of Computer Science, KU Leuven, 2006.

1. K. Deckers,
   Gauss-Kronrod quadrature formulae based on the zeros of Chebyshev orthogonal rational functions. (Slides).
   Invited talk at the conference Recent Advances in Scientific Computation, Santa Margherita di Pula, Italy, May 29, 2019.
2. K. Deckers,
   Numerical integration based on rational interpolation. (Slides).
   Invited talk at the Séminaire EDP de l'Institut Elie Cartan de Lorraine, Metz, France, December 22, 2017.
3. K. Deckers,
   Christoffel-Darboux-type Formulae for Orthonormal Rational Functions and Applications. (Slides).
   Invited talk at the Workshop SIGMA'2016, CIRM, Marseille, France, October 31, 2016.
4. K. Deckers,
   A numerical solution of the constrained weighted energy problem.
   Presentation at the Department of Mathematics, KU Leuven, Belgium, April 4, 2016.
5. K. Deckers,
   Automatic Numerical Integration based on Rational Interpolation.
   Presentation at the Laboratoire Paul Painlevé (Journée de l'équipe ANEDP), Laboratoire de Mathématiques, Lille1, France, January 28, 2016.
6. K. Deckers,
   Christoffel-Darboux-type Formulae for Orthonormal Rational Functions and Asymptotics.
   Invited talk at the 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-13), Maryland, USA, June 4, 2015.
7. K. Deckers,
   Asymptotics for orthonormal rational functions on the interval.
   Invited talk at the Journée Scientifique SMAI-SIGMA, Université Paris VI, Paris, France, November 15, 2013.
8. K. Deckers,
   A rational variant of Fejér's quadrature rule with arbitrary complex poles.
   Invited talk at the School of Mathematics, University of Kent, Canterbury, UK, September 17, 2013.
9. K. Deckers,
   Rational quasi-Radau quadrature rules on the interval with positive weights (Slides).
   Invited talk at the Workshop on orthogonal polynomials and rational functions and related topics, Departamento de Análisis Matemático, Universidad de La Laguna, Tenerife, Spain, February 4, 2013.
10. B. Beckermann, K. Deckers, and M. Pranić.
    On the computation of orthogonal rational functions.
    Presentation at the Congreso de la Real Sociedad Matemática Española, Santiago de Compostela, Spain, January 21-25, 2013.
11. K. Deckers,
    Convergence of rational interpolatory quadrature rules (Slides).
    Invited talk at the Séminaire Calcul Formel, Université de Limoges, Faculté des sciences et techniques, Limoges, France, November 22, 2012.
12. K. Deckers,
    Convergence of rational interpolatory quadrature rules.
    Invited talk at the 3rd Dolomites workshop on constructive approximation and applications, Alba di Canazei, Italy, September 9-14, 2012.
13. K. Deckers,
    Rational Lanczos and short term recurrence relations based on orthogonal rational functions (Slides).
    Invited talk at the 3rd Dolomites workshop on constructive approximation and applications, Alba di Canazei, Italy, September 9-14, 2012.
14. K. Deckers and A. Bultheel
    Quadrature rules based on rational interpolation.
    Presentation at the 1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Liège, Belgium, June 6-8, 2012.
15. K. Deckers,
    Christoffel functions and universality limits associated with orthogonal rational functions (Slides).
    Invited talk at the Séminaires d'Analyse et Géométrie du LATP, Université de Provence, Centre de Mathématiques et Informatique, Marseille, France, June 4, 2012.
16. K. Deckers,
    Interpolation rationnelle quasi-optimale sur un intervalle à pôles fixes (Slides).
    Invited talk at the Séminaires Analyse numérique, Laboratoire Paul Painlevé, Laboratoire de Mathématiques, Lille, France, February 23, 2012.
17. K. Deckers,
    Christoffel functions and universality limits for orthogonal rational functions.
    Invited talk at the seminar series Dept. of Mathematics, KU Leuven, November 9, 2011.
18. K. Deckers,
    Asymptotics for Christoffel functions based on orthogonal rational functions (Slides).
    Invited talk at the International Conference on Scientific Computing, S. Margherita di Pula, Sardinia, Italy, October 10-14, 2011.
19. K. Deckers, M.J. Cantero, L. Moral, and L. Velázquez,
    A special class of orthogonal rational functions on the unit circle, including the associated rational functions.
    Presentation at the conference Complex Analysis, Operator Theory, and Approximation, Johannes Kepler University, Linz, Austria, July 24-29, 2011.
20. K. Deckers and D.S. Lubinsky,
    Asymptotics for Christoffel functions based on orthogonal rational functions (Slides).
    Invited talk at the International Symposium in Approximation Theory, Nashville, Tennessee, USA, May 17-21, 2011.
21. K. Deckers,
    Asymptotics for orthonormal rational functions on the interval (Slides).
    Invited talk at the Approximation Theory and Harmonic Analysis Workshop, Kennesaw, Georgia, USA, May 14-15, 2011.
22. K. Deckers,
    Orthogonal rational functions and rational Gauss-type quadrature rules (Slides).
    Invited talk at the Seminars and Colloquia, School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia, USA, April 6, 2011.
23. K. Deckers, A. Bultheel, and J. Van Deun,
    Rational Gauss-type quadrature formulas with a prescribed node anywhere on the real line (Slides).
    Presentation at the I Jaen Conference on Approximation Theory, Ubeda, Jaen, Spain, July 4-9, 2010.
24. K. Deckers, A. Bultheel, and F. Perdomo-Pio,
    Positive rational interpolatory quadrature rules on the interval and the complex unit circle with preassigned nodes (Slides).
    Presentation at the I Jaen Conference on Approximation Theory, Ubeda, Jaen, Spain, July 4-9, 2010.
25. A. Bultheel, R. Cruz-Barroso, K. Deckers, P. González-Vera, and F. Perdomo-Pio,
    Positive rational interpolatory quadrature formulas on the unit circle and the interval (Slides).
    Presentation at the conference Approximation and extrapolation of convergent and divergent sequences and series, CIRM, Luminy, France, September 28 - October 2, 2009.
26. K. Deckers,
    A rational variant of Fejér's quadrature rule with arbitrary complex poles (Slides).
    Presentation at the 2nd Dolomites workshop on constructive approximation and applications, Alba di Canazei, Italy, September 4-9, 2009.
27. A. Chesnokov, K. Deckers, and M. Van Barel,
    A numerical solution of the constrained weighted energy problem and its relation to rational Lanczos iterations.
    Presentation at the 2nd Dolomites workshop on constructive approximation and applications, Alba di Canazei, Italy, September 4-9, 2009.
28. A. Chesnokov, K. Deckers, and M. Van Barel,
    A numerical solution of the constrained weighted energy problem and its relation to rational Lanczos iterations (Slides).
    Invited talk at the Seminar on Orthogonality, Approximation Theory and Applications, Escuela Politécnica Superior, Universidad Carlos III de Madrid, Spain, June 18, 2009.
29. K. Deckers,
    A rational variant of Fejér's quadrature rule with arbitrary complex poles.
    Invited talk at the Seminario Rubio de Francia, Institutio Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, Spain, June 10, 2009.
30. K. Deckers and A. Bultheel,
    Orthogonal rational functions and rational modifications of a measure (Slides).
    Presentation at the seminar series Dept. of Mathematics, KU Leuven, September 30, 2008.
31. K. Deckers and A. Bultheel,
    Orthogonal rational functions, associated rational functions and functions of the second kind (Slides).
    Presentation at the World Congress on Engineering; Internatl. Conf. of Applied and Engineering Mathematics (ICAEM VII), London, UK, July 2-4, 2008.
32. K. Deckers and A. Bultheel,
    Rational Krylov sequences and orthogonal rational functions (Slides).
    Presentation at the 13th Internatl. Conf. on Computational and Applied Mathematics (ICCAM), Ghent, Belgium, July 7-11, 2008.
33. K. Deckers and A. Bultheel,
    Rational Krylov sequences and orthogonal rational functions (Poster).
    Poster presented at the 3ièmes Journées Approximation, Lille, May 15-16, 2008.
34. K. Deckers, J. Van Deun, and A. Bultheel,
    Computing rational Gauss-Chebyshev quadrature formulas with complex poles (Slides).
    The Fifth International Conference on Engineering Computational Technology, Las Palmas de Gran Canaria, Spain, September 12-15, 2006.

PhD Thesis

• Orthogonal Rational Functions: Quadrature, Recurrence and Rational Krylov, KU Leuven, February 2009.

Conferences and Research Stays

• September 19, 2019:
  A one-day Approximation meeting (Honoring Professor Marc Prévost),
  Calais, France.
• September 6, 2019:
  7th OPSFOTA,
  Leuven, Belgium.
• May 27-29, 2019:
  Recent Advances in Scientific Computation,
  Santa Margherita di Pula, Italy.
• May 31 - June 1, 2018:
  International conference on Approximation and Matrix Functions,
  Lille, France.
• May 30, 2017:
  1rst RENALNACA (RENcontre en Algèbre Linéaire Numérique Amiens- CAlais),
  Amiens, France.
• October 31 - November 4, 2016:
  Workshop SIGMA'2016: SIGNAL, IMAGE, GEOMETRY, MODELLING, APPROXIMATION,
  Marseille, France.
• May 20, 2016:
  5èmes Journées Approximation,
  Lille, France.
• June 1-5, 2015:
  The 13th International Symposium on Orthogonal Polynomials, Special Functions and Applications (OPSFA-13),
  Gaithersburg, Maryland, USA.
• January 20-24, 2014:
  An International Symposium on Orthogonality, Quadrature and Related Topics,
  In memory of Prof. Dr. Pablo González Vera,
  Tenerife, Spain.
• November 15, 2013:
  Journée Scientifique SMAI-SIGMA 2013,
  Paris, France.
• October 28-31, 2013:
  Nord Pas de Calais/Belgium congress of mathematics,
  Valenciennes, France, and Mons, Belgium.
• September 17-18, 2013:
  Kent - Lille seminar session,
  Canterbury, United Kingdom.
• May 15-17, 2013:
  International Spring School on Matrix Functions and their applications (SSMF2013),
  Lille, France.
• January 31 - February 5, 2013:
  Workshop on the occasion of the PhD Dissertation of Francisco José Perdomo Pío, Departamento de Análisis Matemático, Universidad de La Laguna,
  Tenerife, Spain.
• September 9-14, 2012:
  The 3rd Dolomites Workshop on Constructive Approximation and Applications (DWCAA12),
  Alba di Canazei, Trento, Italy.
• July 9-13, 2012:
  International Congress on Computational and Applied Mathematics (ICCAM 2012),
  Gent , Belgium.
• July 2-3, 2012:
  Approximation Days 2012,
  Leuven, Belgium.
• June 28-29, 2012:
  4èmes Journées Approximation,
  Lille, France.
• June 11-15, 2012:
  Short research stay at the Laboratoire Paul Painlevé, Laboratoire de Mathématiques,,
  Lille, France.
• June 6-8, 2012:
  1st Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies,
  Liège, Belgium.
• October 10-14, 2011:
  International Conference on Scientific Computing (SC2011),
  A Conference to celebrate the 70th birthday of Claude Brezinski and Sebastiano Seatzu and the 20th anniversary of the Springer journal Numerical Algorithms,
  S. Margherita di Pula, Sardinia, Italy.
• May 17-21, 2011:
  International Symposium in Approximation Theory,
  Nashville, Tennessee, USA.
• May 14-15, 2011:
  Approximation Theory and Harmonic Analysis Workshop,
  Kennesaw, Georgia, USA.
• February 1 - July 31, 2011:
  Research stay at the School of Mathematics, Georgia Institute of Technology,
  Atlanta, Georgia, USA.
• July 4-9, 2010:
  I Jaen Conference on Approximation Theory,
  Ubeda, Jaen, Spain.
• September 4-9, 2009:
  2nd Dolomites workshop on constructive approximation and applications (DWCAA09),
  Alba di Canazei, Italy.
• July 20-25, 2009:
  10th International Symposium on Orthogonal Polynomials, Special Functions and Applications,
  Leuven, Belgium.
• June 3-30, 2009:
  Research stay at the Departamento de Matemática Aplicada, Universidad de Zaragoza,
  Zaragoza, Spain.
• December 15-16, 2008:
  Rolling Waves in Leuven 2008,
  An international workshop on the occasion of Adhemar Bultheel's 60th birthday,
  Leuven, Belgium.
• November 1-30, 2008:
  Research stay at the Departamento de Análisis Matemático, Universidad de La Laguna,
  Tenerife, Spain.
• July 07-11, 2008:
  The 13th International Congress on Computational and Applied Mathematics (ICCAM 2008),
  Ghent, Belgium.
• July 02-04, 2008:
  The 2008 International Conference of Applied and Engineering Mathematics (ICAEM 2008),
  London, United Kingdom.
• May 19-20, 2008:
  Workshop on Orthogonal Polynomials and Special Functions,
  On the occasion of the 50th birthday of Walter Van Assche,
  Leuven, Belgium.
• May 15-16, 2008:
  3ièmes Journées Approximation,
  Lille, France.
• October 29-30, 2007:
  Symposium on "The Birth of Numerical Analysis",
  Leuven, Belgium.
• September 12-15, 2006:
  The Fifth International Conference on Engineering Computational Technology (ECT2006),
  Las Palmas de Gran Canaria, Spain.