Given f ∈ C [−1, 1], let Hn, 3(f, x) denote the (0,1,2) Hermite-Fejér interpolation polynomial of f based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |Hn, 3(f, x) − f(x)|. Further, we demonstrate a method of combining the divergent Lagrange and (0,1,2) interpolation methods on the Chebyshev nodes to obtain a convergent rational interpolatory process.
The absorption spectrum of CF2 in the 2 500 Å region has been photographed at high dispersion, and the rotational structure of a number of bands has been analyzed. The analysis of the well-resolved subbands establishes that these are perpendicular- rather than parallel-type bands, as previously assigned. Further analysis shows that the upper and lower electronic states are of 1B1 and 1A1symmetries respectively, corresponding to a transition moment that is perpendicular to the plane of the molecule. In the upper electronic state, r0(CF) = 1.32 Å and [Formula: see text], while in the ground state, r0(CF) = 1.300 Å and [Formula: see text]. An investigation of the vibrational structure of the band system has shown that the vibrational numbering in ν2′ must be increased by one unit from earlier assignments, thus placing the 000–000 band near 2 687 Å (37 220 cm−1). A search between 1 300 and 8 500 Å showed two new band systems near 1 350 and 1 500 Å which have been assigned tentatively to the CF2 molecule.
On Hermite-Fejér type interpolation on the Chebyshev nodes
