New methods for numerical evaluation of ultra-high degree and order associated Legendre functions
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F22%3A43966135" target="_blank" >RIV/49777513:23520/22:43966135 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007/s11200-022-0830-9" target="_blank" >https://link.springer.com/article/10.1007/s11200-022-0830-9</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11200-022-0830-9" target="_blank" >10.1007/s11200-022-0830-9</a>
Alternative languages
Result language
angličtina
Original language name
New methods for numerical evaluation of ultra-high degree and order associated Legendre functions
Original language description
We improve the precision and computation speed of the fully-normalized associated Legendre functions (fnALFs) for ultra-high degrees and orders of spherical harmonic transforms. We take advantage of their numerical behaviour of and propose two new methods for solving an underflow/overflow problem in their calculation. We specifically discuss the application of the two methods in the fixed-order increasing-degree recursion computation technique. The first method uses successive ratios of fnALFs and the second method, called the Midway method, starts iteration from tiny initial values, which are still in the range of the IEEE double-precision environment, rather than from sectorial fnALFs. The underflow/overflow problem in the successive ratio method is handled by using a logarithm-based method and the extended range arithmetic. We validate both methods using numerical tests and compare their results with the X-number method in terms of precision, stability, and speed. The results show that the relative precision of the proposed methods is better than 10-9 for the maximum degree of 100000, compared to results derived by the high precision Wolfram’s Mathematica software. Average CPU times required for evaluation of fnALFs over different latitudes demonstrate that the two proposed methods are faster by about 10-30% and 20-90% with respect to the X-number method for the maximum degree in the range of 50-65000.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10508 - Physical geography
Result continuities
Project
<a href="/en/project/GA21-13713S" target="_blank" >GA21-13713S: Uncertainty estimates for integral transformations in geodesy</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Studia Geophysica et Geodaetica
ISSN
0039-3169
e-ISSN
1573-1626
Volume of the periodical
66
Issue of the periodical within the volume
3-4
Country of publishing house
DE - GERMANY
Number of pages
17
Pages from-to
81-97
UT code for WoS article
000883430500001
EID of the result in the Scopus database
2-s2.0-85141979721