Numerical Analysis, Probability and Statistics by ylx48163

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									Numerical Analysis, Probability and Statistics

                                    CMUP

                                  21/07/2008




CMUP (21/07/2008)   Numerical Analysis, Probability and Statistics   1 / 10
People – Members (pluri-anual 2003–2006; 2007–2010)




    Filomena Dias d’Almeida
    Margarida Brito
    Ana Cristina Moreira de Freitas
       e
    Jos´ Matos
    Alexandra Ramos – (since 2004)
     e
    Z´lia da Rocha – (up to 2006)
             a
    Maria Jo˜o Sampaio Rodrigues
    Paulo B. Vasconcelos




     CMUP (21/07/2008)     Numerical Analysis, Probability and Statistics   2 / 10
Achievements 2003–2006

    Development of PFSI method, for the computation of eigenpairs of
    quasi-diagonal matrices. Proof of convergence theorems and implementation.
    Application of the defect correction technique to the development of a
    method for the computation of spectral elements of integral operators.
    Serial and parallel codes for the computation of approximate solutions of
    integral equations using projection-iterative refinement techniques, with
    optimized linear computational kernels and sparse structures.
    Computational aspects of FPA for series of orthogonal polynomials: recursive
    algorithms, software development and study of numerical behaviour.
    Symbolic computation for the study of the characterizations and properties of
    orthogonal polynomials.
    Recurrence relations in the coefficients of rational approximation; its
    implementation and application to approximate Fourier series in orthogonal
    polynomials.
    Development of algorithms for the calculation of the coefficients of Tau
    method approximants for the solution of n-dimensional partial derivatives
    problems.

     CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics      3 / 10
Achievements 2003–2006

    Asymptotic properties of a geometric-type estimator and of adequate
    bootstrapped versions for estimating exponential-tail coefficients.
    Confidence bounds for the adjustment coefficient in the Sparre Andersen
    model for an insurance company.
    Characterization of the uniform almost sure consistency of simple
    nonparametric estimators of the isobars.
    Construction and study of score tests of independence in multivariate extreme
    values and applications.
    Derivation and characterization of models for dependence within joint tail
    regions.

Publications
    13 papers published in international peer reviewed journals (Linear Algebra
    Appl., J. Comput. Appl. Math., J. Math. Anal. Appl., Commun. Pure Appl.
    Anal., Insurance Math. Econom., Extremes, . . . ).
    9 papers published in books or proceedings of conferences.

      CMUP (21/07/2008)     Numerical Analysis, Probability and Statistics    4 / 10
Conferences
   Encontro Nacional da SPM, co-organized, Porto, 2004 and organization of
   the Thematic Sessions on Numerical Analysis and Probability and Statistics.
   Parallel Numerical Algorithms — Topic 10 of Europar2005, Lisbon, 2005.

   Eigenvalue Problems: Software and Applications - EPSA2007, Satellite
   Conference of ICIAM07 - 6th International Congress on Industrial and
   Applied Mathematics, FCUP, 2007.
   Spectral Computations for Integral Operators, Minisymposium
   IC/MP/023/S/671 of ICIAM07, Zurich, Switzerland, 2007.
                            ca        a
   XIV Jornadas de Classifica¸˜o e An´lise de Dados, co-organized, ISEP, 2007.
   XV Congresso Anual da Sociedade Portuguesa de Estat´   ıstica (SPE), ISCTE,
   Lisbon 2007 (participation in the Scientific and Executive Committee).
   56th Session of the International Statistical Institute (ISI), Lisbon, 2007
   (participation in the Local Programme Committee).
   Bernoulli Society satellite meeting of ISI’2007: Probability and Statistics in
   Science and Technology, Porto 2007 (participation in the Scientific
   Committee).

     CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics          5 / 10
Minicourses, seminars
    Minicourses:
      ◮   Mathematical Methods in Insurance, Hansjoerg Albrecher, Graz University of
          Technology & RICAM, Austria (2006).
      ◮   Approximate Solutions of Second Kind Integral Equations, Rekha Kulkarni,
          Indian Institute of Technology, Bombay, India (2006).
      ◮   Accelerated Spectral Approximation, Balmohan Limaye, Indian Institute of
          Technology, Bombay, India (2005).
      ◮     o           a                           a                  o
          T´picos em c´lculo de alto desempenho: c´lculo de valores pr´prios e
                                                       co       ıficas, Osni Marques,
          ferramentas para o desenvolvimento de aplica¸˜es cient´
          Lawrence Berkeley National Laboratory (2004).
    Numerical Analysis, Probability and Statistics seminar, including: ”Working
    Day on Orthogonal Polynomials and its Applications” (2006);
    ”Working Day on Approximation Theory and Applications” (2003).




     CMUP (21/07/2008)        Numerical Analysis, Probability and Statistics       6 / 10
Graduate student training
    4 PhD concluded (2003-2006):
              e                    e
    2003: Jos´ Matos supervisor: Z´lia da Rocha; co-supervisor: Ana Cristina
    Matos, Univ. Lille I.
          ˆ                                               e
    2004: Angela Macedo and Isabel Nicolau, supervisor: Z´lia da Rocha;
    co-supervisor: Pascal Maroni (CNRS - PARIS VI).
    2005: Ana Cristina Moreira de Freitas, supervisor: Margarida Brito.
    Current PhD students: Manuel Cruz (supervised by Filomena d’Almeida and
                                        a
    Paulo B. Vasconcelos), Maria do Ros´rio Fernandes (supervised by Filomena
                                         e
    d Almeida and Mario Ahues, Universit´ de Saint Etienne, France), Paulo
                                                              a
    Mota (supervised by Paulo B. Vasconcelos and J. M. Varej˜o, Faculdade de
    Economia UP).
    8 MSc thesis supervised (2003–2006).




     CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics   7 / 10
Research projects




                                                           c˜
    Parallelization of algorithms for integral problems, Ac¸oes Integradas
    Luso-Francesas F13/03, 2003-04.
    GRIDUP of IRICUP (since 2005).
    Methods for spectral computations and their implementation in parallel
                   c˜
    computers, Ac¸oes Integradas Luso-Espanholas, FEP, FEUP, ISEP-IPP and
                                     a                 o
    Departamento de Sistemas Inform´ticos y Computaci´n (DSIC), Universidad
    Politecnica de Valencia (UPV), 2007-08.
                 o                       a
    LEMA, Laborat´rio de Engenharia Matem´tica, IPP/PADInv 2007 ISEP,
    CMUP.




     CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics   8 / 10
Research objectives 2007–2010

    To propose prove and test hybrid methods for spectral computations of
    integral operators, based on inner/outer iteration, where inner iteration is
    simple and the outer is more powerful, based, for instance, on projection
    methods. Implemementation of these methods on parallel machines and, if
    possible, on mixed precision machines that have single precision arithmetic
    unit much faster than double precision unit.
    To apply defect correction techniques to the linearization of a quadratic non
    symmetric eigenvalue problem. Application of such methods in the study of
    instabilities in the brake systems, in mechanical engineering.
    Comparison of Perturbed Fixed Slope Iteration (PFSI) with Jacobi-Davidson
    and Davidson methods.
    Application of the Tau method to integral equations and to partial differential
    equations and comparison with other spectral methods.
    Study of the accuracy and stability of numerical algorithms in rational
    approximation.
    Discuss the connection between fiscal policies and economic growth in a
    monetary union: modeling and simulation.

     CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics         9 / 10
   To develop end extend previous research work on tail estimation problems, in
   particular, to dependent cases. Applications to risk theory.
   To characterize the extremal behaviour of some chaotic dynamical systems.
   Modelling and study of the joint tails for multivariate observations.
   Applications to financial data. Markov modelling of the within time series
   dependence. Study of the componentwise maxima generalized results for the
   bivariate normal dependence structure.

Achievments
   One Conference Proceedings
   6 Papers published or accepted in international peer reviewed journals (J. R.
   Statist. Soc., B, Insurance Math. Econom., Int. Econ. J . . . );
   6 papers published or accepted in books or proceedings of conferences.
   Organization of 2 meetings (2008).




    CMUP (21/07/2008)      Numerical Analysis, Probability and Statistics     10 / 10

								
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