scholarly journals Lagrangian Interpolation at the Chebyshev Points xn,     cos (  /n),   = 0(1)n; some Unnoted Advantages

1972 ◽  
Vol 15 (2) ◽  
pp. 156-159 ◽  
Author(s):  
H. E. Salzer
Keyword(s):  
Chebyshev Points ◽  
Lagrangian Interpolation

scholarly journals Hermite-Fejer interpolation at the ‘practical’ Chebyshev nodes

1973 ◽  
Vol 9 (3) ◽  
pp. 379-390
Author(s):  
R.D. Riess
Keyword(s):  
Continuous Functions ◽  
Negative Results ◽  
Chebyshev Nodes ◽  
Chebyshev Points ◽  
Uniformly Convergent ◽  
Lagrangian Interpolation

Berman has raised the question in his work of whether Hermite-Fejér interpolation based on the so-called “practical” Chebyshev points, , 0(1)n, is uniformly convergent for all continuous functions on the interval [−1, 1]. In spite of similar negative results by Berman and Szegö, this paper shows this result is true, which is in accord with the great similarities of Lagrangian interpolation based on these points versus the points , 1(1)n.

Tables for Lagrangian Interpolation using Chebyshev Points.

1982 ◽  
Vol 39 (160) ◽  
pp. 743
Author(s):  
Herbert E. Salzer ◽  
Norman Levine ◽  
Saul Serben
Keyword(s):  
Chebyshev Points ◽  
Lagrangian Interpolation

scholarly journals Covering and separation of Chebyshev points for non-integrable Riesz potentials

2018 ◽  
Vol 46 ◽  
pp. 19-44 ◽  
Author(s):  
A. Reznikov ◽  
E. Saff ◽  
A. Volberg
Keyword(s):  
Riesz Potentials ◽  
Chebyshev Points

scholarly journals A Library of Standard Programmes for Constructing Numerical Theories for Studying the Motion and Evolution of the Orbits of the Minor Bodies of the Solar System

1972 ◽  
Vol 45 ◽  
pp. 86-89 ◽  
Author(s):  
N. A. Bokhan
Keyword(s):  
Solar System ◽  
Variable Step ◽  
Rectangular Coordinates ◽  
Lagrangian Interpolation ◽  
Orbit Improvement ◽  
Nongravitational Effects

At the Institute for Theoretical Astronomy we have formed a library containing about 120 standard computer programmes. They include calculation of rectangular coordinates and velocities from elements, Lagrangian interpolation, and orbit improvement by the Eckert-Brouwer method. For the investigation of the motions of the minor bodies of the solar system we have constructed a programme for integration with a variable step and making allowance for perturbations by all the major planets and for nongravitational effects. The calculation of the perturbations is carried out using Herrick's vector parameters by the method of variation of arbitrary constants. The programme has been used for studying the motion of P/Encke.

Lagrangian interpolation and differentiation

1983 ◽  
Vol 36 (13) ◽  
pp. 447-448
Author(s):  
F. Calogero
Keyword(s):  
Lagrangian Interpolation

scholarly journals Vandermonde matrices on Chebyshev points

1998 ◽  
Vol 283 (1-3) ◽  
pp. 205-219 ◽  
Author(s):  
A. Eisinberg ◽  
G. Franzé ◽  
P. Pugliese
Keyword(s):  
Vandermonde Matrices ◽  
Chebyshev Points

General anonymous key broadcasting via Lagrangian interpolation

2008 ◽  
Vol 2 (3) ◽  
pp. 79
Author(s):  
Ł. Krzywiecki ◽  
M. Kutyłowski ◽  
M. Nikodem
Keyword(s):  
Lagrangian Interpolation

scholarly journals IMERG V06: Changes to the Morphing Algorithm

2019 ◽  
Vol 36 (12) ◽  
pp. 2471-2482 ◽  
Author(s):  
Jackson Tan ◽  
George J. Huffman ◽  
David T. Bolvin ◽  
Eric J. Nelkin
Keyword(s):  
Large Scale ◽  
Numerical Models ◽  
Precipitable Water ◽  
Passive Microwave ◽  
Precipitation Field ◽  
Motion Vectors ◽  
Surface Precipitation ◽  
General Improvement ◽  
Lagrangian Interpolation ◽  
Cloud Tops

AbstractAs the U.S. Science Team’s globally gridded precipitation product from the NASA–JAXA Global Precipitation Measurement (GPM) mission, the Integrated Multi-Satellite Retrievals for GPM (IMERG) estimates the surface precipitation rates at 0.1° every half hour using spaceborne sensors for various scientific and societal applications. One key component of IMERG is the morphing algorithm, which uses motion vectors to perform quasi-Lagrangian interpolation to fill in gaps in the passive microwave precipitation field using motion vectors. Up to IMERG V05, the motion vectors were derived from the large-scale motions of infrared observations of cloud tops. This study details the changes introduced in IMERG V06 to derive motion vectors from large-scale motions of selected atmospheric variables in numerical models, which allow IMERG estimates to be extended from the 60°N–60°S latitude band to the entire globe. Evaluation against both instantaneous passive microwave retrievals and ground measurements demonstrates the general improvement in the precipitation field of the new approach. Most of the model variables tested exhibited similar performance, but total precipitable water vapor was chosen as the source of the motion vectors for IMERG V06 due to its competitive performance and global completeness. Continuing assessments will provide further insights into possible refinements of this revised morphing scheme in future versions of IMERG.

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