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  • 41  (4)
  • Springer  (4)
  • American Geophysical Union
  • American Society of Hematology
  • BioMed Central
  • Blackwell Publishing Ltd
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Verlag/Herausgeber
  • Springer  (4)
  • American Geophysical Union
  • American Society of Hematology
  • BioMed Central
  • Blackwell Publishing Ltd
Erscheinungszeitraum
  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Numerical algorithms 3 (1992), S. 201-209 
    ISSN: 1572-9265
    Schlagwort(e): AMS 15 ; 41 ; Orthogonal polynomials ; Laurent polynomials ; T-fractions ; Padé approximants
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract This paper is concerned with double sequencesC={C n} n =−∞/∞ of Hermitian matrices with complex entriesC n ∈M s×s ) and formal Laurent seriesL 0(z)=−Σ k=1 ∞ C −k z k andL ∞(z)=Σ k=0 ∞ C k z −k . Making use of a Favard-type theorem for certain sequences of matrix Laurent polynomials which was obtained previously in [1] we can establish the relation between the matrix counterpart of the so-calledT-fractions and matrix orthogonal Laurent polynomials. The connection with two-point Padé approximants to the pair (L 0,L ∞) is also exhibited proving that such approximants are Hermitian too. Finally, error formulas are also given.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Advances in computational mathematics 5 (1996), S. 297-328 
    ISSN: 1572-9044
    Schlagwort(e): Distribution functions ; integration rules ; interpolation nodes ; Szegö polynomials ; 41 ; 65D
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, quadrature formulas on the unit circle are considered. Algebraic properties are given and results concerning error and convergence established. Finally, numerical experiments are carried out.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Numerical algorithms 15 (1997), S. 167-192 
    ISSN: 1572-9265
    Schlagwort(e): Matrix Padé Approximation ; rationality ; minimum degrees ; uniqueness ; 65 ; 41 ; 15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In many applications it is of major interest to decide whether a given formal power series with matrix-valued coefficients of arbitrary dimensions results from a matrix-valued rational function. As the main result of this paper we provide an answer to this question in terms of Matrix Padé Approximants of the given power series. Furthermore, given a matrix rational function, the “smallest” degrees of the matrix polynomials which represent it are not necessarily unique. Therefore we study a certain minimality-type, that is, minimum degrees. We aim to obtain all the minimum degrees for the polynomials which represent the function as equivalents. In addition, given that the rational representation of the function for the same pair of degrees need not be unique, we have obtained conditions to study the uniqueness of said representation. All the results obtained are presented graphically in tables setting out the above information. They lead to a number of properties concerning special structures, staired blocks, in the Padé Table.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
    BibTip Andere fanden auch interessant ...
  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Numerical algorithms 9 (1995), S. 379-395 
    ISSN: 1572-9265
    Schlagwort(e): Transfer-function model ; Padé approximation ; ε-algorithm ; 41 ; 62 ; 65 ; 90
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract The aim of this paper is to apply an algorithm related to the rational approximation for the identification of the lag structure in a transfer-function model. In fact, we apply the ε-algorithm proposed by Berlinet [3–5] to determine the polynomial orders in univariate and multivariate ARMA models. Furthermore, it has been proposed by Berlinet [5], González and Cano [13, 14] and González et al. [15] for a transfer-function model with one input and multiple inputs, respectively. The main contribution in this paper concerns the study of the relative significance of the elements in the ε-algorithm table, in the same way as that given by Berlinet and Francq [7] for ARMA models, to confirm the pattern used to specify the model. Two examples will be considered, namely, the sales series M [8] and a simulated model [20]. A comparison is also made between the results of the ε-algorithm and the corner method generally used in the econometric literature. Although the ε-algorithm requires a more advanced theory in Numerical Analysis, it can be applied in a more simple way than the corner method.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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