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140122 ||| eng |
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|a 9783034893060
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|a Bultheel, A.
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| 245 |
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|a Laurent Series and their Padé Approximations
|h Elektronische Ressource
|c by A. Bultheel
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| 250 |
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|a 1st ed. 1987
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| 260 |
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|a Basel
|b Birkhäuser
|c 1987, 1987
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| 300 |
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|a XI, 276 p
|b online resource
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|a 8.4 ?? paramaters (diagonal path) -- 8.5 Some dual results -- 8.6 Relation with classical algorithms -- 9. Biorthogonal polynomials, quadrature and reproducing kernels -- 9.1 Biorthogonal polynomials -- 9.2 Interpolatory quadrature methods -- 9.3 Reproducing kernels -- 9.4 Other orthogonality relations -- 10. Determinant expressions and matrix interpretations -- 10.1 Determinant expressions -- 10.2 Matrix interpretations -- 11. Symmetry Properties -- 11.1 Symmetry for F(z) and
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|a 2. Introduction -- 2.1 Classical Padé approximation -- 2.2 Toeplitz and Hankel systems -- 2.3 Continued fractions -- 2.4 Orthogonal polynomials -- 2.5 Rhombus algorithms and convergence -- 2.6 Block structure -- 2.7 Laurent-Padé approximants -- 2.8 The projection method -- 2.9 Applications -- 2.10 Outline -- 3. Moebius transforms, continued fractions and Padé approximants -- 3.1 Moebius transforms -- 3.2 Flow graphs -- 3.3 Continued fractions (CF) -- 3.4 Formal series -- 3.5 Padé approximants -- 4. Two algorithms -- 4.1 Algorithm 1 -- 4.2 Algorithm 2 -- 5. All kinds of Padé Approximants -- 5.1 Padé approximants -- 5.2 Laurent-Padé approximants -- 5.3 Two-point Padé approximants -- 6. Continued fractions -- 6.1 General observations -- 6.2 Some special cases -- 7. Moebius transforms -- 7.1 General observations -- 7.2 Some special cases -- 8. Rhombus algorithms -- 8.1 The ab parameters (sawtooth path) -- 8.2. The FG parameters (row path) -- 8.3. A staircase path --
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| 653 |
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|a Humanities and Social Sciences
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| 653 |
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|a Humanities
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| 653 |
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|a Social sciences
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| 041 |
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7 |
|a eng
|2 ISO 639-2
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| 989 |
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|b SBA
|a Springer Book Archives -2004
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| 490 |
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|a Operator Theory: Advances and Applications
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| 028 |
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|a 10.1007/978-3-0348-9306-0
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| 856 |
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|u https://doi.org/10.1007/978-3-0348-9306-0?nosfx=y
|x Verlag
|3 Volltext
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|a 001.3
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|a 300
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| 520 |
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|a The Pade approximation problem is, roughly speaking, the local approximation of analytic or meromorphic functions by rational ones. It is known to be important to solve a large scale of problems in numerical analysis, linear system theory, stochastics and other fields. There exists a vast literature on the classical Pade problem. However, these papers mostly treat the problem for functions analytic at 0 or, in a purely algebraic sense, they treat the approximation of formal power series. For certain problems however, the Pade approximation problem for formal Laurent series, rather than for formal power series seems to be a more natural basis. In this monograph, the problem of Laurent-Pade approximation is central. In this problem a ratio of two Laurent polynomials in sought which approximates the two directions of the Laurent series simultaneously. As a side result the two-point Pade approximation problem can be solved. In that case, two series are approximated, one is a power series in z and the other is a power series in z-l. So we can approximate two, not necessarily different functions one at zero and the other at infinity
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