Matrix interpretation of multiple orthogonality

Abstract  In this work we give an interpretation of a (s (d + 1 ) + 1)-term recurrence relation in terms of type II multiple orthogonal polynomials. We rewrite this recurrence relation
in matrix form and we obtain a three-term recurrence relation for vector polynomials with matrix coefficients. We present
a matrix interpretation of the type II multi-orthogonality conditions. We state a Favard type theorem and the expression for
the resolvent function associated to the vector of linear functionals. Finally a reinterpretation of the type II Hermite-Padé
approximation in matrix form is given.

• Content Type Journal Article
• Category Original Paper
• DOI 10.1007/s11075-009-9355-3
• Authors
  
  
  • Amílcar Branquinho, University of Coimbra CMUC, Department of Mathematics Largo D. Dinis 3001-454 Coimbra Portugal
  • Luis Cotrim, Polytechnic Institute of Leiria “Acção do Prodep” reference 5.3/C/00187.010/03, School of Technology and Management Campus 2—Morro do Lena—Alto do Vieiro 2411-901 Leiria Portugal
  • Ana Foulquié Moreno, Universidade de Aveiro UI Matemática e Aplicações from University of Aveiro, Departamento de Matemática Campus de Santiago 3810 Aveiro Portugal
  
  

• Journal Numerical Algorithms
• Online ISSN 1572-9265
• Print ISSN 1017-1398

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Original source : http://www.springerlink.com/content/41444303434066...