Shafer, R.E., On quadratic approximation, SIAM J. Numer. Anal., 11 (1974), 447-60. Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Quadratic Hermite-Padé Polynomials Associated with the.. - Stahl (Correct)
.... for instance, 11, 12, 13] 5] 9] and in approximation theory (cf. the survey about publications in approximation theory in [3] and a survey about asymptotic results in [1] Detailed studies of quadratic approximants and especially of the polynomials pn ; q n ; r n have been done in [4] [19], 6] and [7] In [4] among other things, a 4 term recurrence relation together with very precise asymptotic estimates have been proved. While in [4] like in (1.1) only the diagonal case has been considered, the investigation has been extended to the non diagonal situation in [6] and [7] In ....
Shafer, R.E., On quadratic approximation, SIAM J. Numer. Anal., 11 (1974), 447-60.
A Padé-based algorithm for overcoming the Gibbs.. - Driscoll, Fornberg (Correct)
....Fourier Pad method is that irregularities in f introduce features in f and f that Pad approximations do not handle well. Specifically, the use of poles to approximate branch cuts is inefficient. One general technique for better approximating branch cuts is the quadratic Hermite Pad method [1,4,15], in which square root singularities complement the usual Pad poles. However, as we shall soon see, the branch cuts in f and f are logarithmic, not square root, in nature. Our experiments indicate that a Fourier Hermite Pad method improves only slightly on standard FP. 4. Singular ....
R.E. Shafer, On quadratic approximation, SIAM J. Numer. Anal. 11 (1974) 447--460.
Computation of Numerical Padé-Hermite and.. - Cabay, Jones, Labahn (2 citations) (Correct)
....results given in this paper also hold with minor modifications for the field of complex numbers. 2 By convention, a polynomial of degree 1 is the zero polynomial. classical approximation problems such as the algebraic approximants where A t (z) 1; a(z) a(z) 2 ; a(z) k ] see [25] for the special case k = 2) and G 3 J approximants where A t (z) 1; a(z) a 0 (z) Additional examples can be found in [1] Closely related to Pad e Hermite approximants are simultaneous Pad e approximants. A simultaneous Pad e approximant of type n for A(z) is a nontrivial vector [q ....
R. Shafer, On quadratic approximation, SIAM J. Numerical Analysis, 11 (1974), pp. 447--460.
A uniform approach for the fast computation of Matrix-type.. - Beckermann, Labahn (1996) (14 citations) (Correct)
....0 P 2 (z) O(z n 1 n 2 1 ) and hence as a special case we have the classical Pad e approximation problem for a power series f . Hermite Pad e approximation also includes other classical approximation problems such as algebraic approximants (F = 1; f; f 2 ; f m01 ) T ) e.g. [23] for the special case m = 2) and G 3 J approximants (m = 3; F = f 0 ; f; 1) T ) We refer the reader to [1, pp.32 40] for additional examples. More generally, there is the M Pad e approximation problem which requires that P1F vanishes at a given set of knots z 0 ; z 1 ; z N01 , ....
R.E. Shafer, On quadratic approximation, SIAM J. Numerical Analysis 11 (1974) 447460.
Experiments with a Weakly Stable Algorithm for Computing.. - Cabay, Jones (1997) (1 citation) (Correct)
.... and the simultaneous Pad e approximation problems each become the classical Pad e approximation problem for a(z) Pad e Hermite approximation also includes other classical approximation problems such as algebraic approximants with A t (z) 1; a(z) a 2 (z) a k (z) e.g. [Shafer 1974] for the special case k = 2) and G 3 J approximants with A t (z) 1; a(z) a 0 (z) Simultaneous Pad e approximants were first used by Hermite in 1873 in his famous proof of the transcendence of e. Additional examples, along with historical motivations and applications of these ....
Shafer, R. 1974. On quadratic approximation. SIAM J. Numerical Analysis 11, 447--460.
A Stable Algorithm for Multi-dimensional Padé.. - Cabay, Jones, Labahn (1994) (2 citations) (Correct)
....results given in this paper also hold with minor modifications for the field of complex numbers. 2 By convention, a polynomial of degree 1 is the zero polynomial. classical approximation problems such as the algebraic approximants where A t (z) 1; a(z) a(z) 2 ; a(z) k ] see [26] for the special case k = 2) and G 3 J approximants where A t (z) 1; a(z) a 0 (z) Additional examples can be found in [1] Closely related to Pad e Hermite approximants are simultaneous Pad e approximants. A simultaneous Pad e approximant of type n for A(z) is a nontrivial vector [q ....
R. Shafer, On quadratic approximation, SIAM J. Numerical Analysis, 11 (1974), pp. 447--460.
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