Fast and accurate algorithm for the generalized exponential integral Eν(x) for positive real order
We describe an algorithm for the numerical evaluation of the generalized exponential integral E ν ( x ) for positive values of ν and x . A detailed description of the numerical methods used in the algorithm is provided, including error bounds. Different approaches from earlier algorithms are also su...
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| Published in | Numerical algorithms Vol. 77; no. 2; pp. 603 - 630 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.02.2018
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1017-1398 1572-9265 |
| DOI | 10.1007/s11075-017-0331-z |
Cover
| Abstract | We describe an algorithm for the numerical evaluation of the generalized exponential integral
E
ν
(
x
) for positive values of
ν
and
x
. A detailed description of the numerical methods used in the algorithm is provided, including error bounds. Different approaches from earlier algorithms are also summarised. The performance and accuracy of the resulting algorithm is analysed and compared with open-source software packages. This analysis shows that our implementation is competitive and more robust than other state-of-the-art codes. Finally, a brief study of the implementation of
E
ν
(
x
) in arbitrary-precision arithmetic is discussed. |
|---|---|
| AbstractList | We describe an algorithm for the numerical evaluation of the generalized exponential integral Eν(x) for positive values of ν and x. A detailed description of the numerical methods used in the algorithm is provided, including error bounds. Different approaches from earlier algorithms are also summarised. The performance and accuracy of the resulting algorithm is analysed and compared with open-source software packages. This analysis shows that our implementation is competitive and more robust than other state-of-the-art codes. Finally, a brief study of the implementation of Eν(x) in arbitrary-precision arithmetic is discussed. We describe an algorithm for the numerical evaluation of the generalized exponential integral E ν ( x ) for positive values of ν and x . A detailed description of the numerical methods used in the algorithm is provided, including error bounds. Different approaches from earlier algorithms are also summarised. The performance and accuracy of the resulting algorithm is analysed and compared with open-source software packages. This analysis shows that our implementation is competitive and more robust than other state-of-the-art codes. Finally, a brief study of the implementation of E ν ( x ) in arbitrary-precision arithmetic is discussed. |
| Author | Navas-Palencia, Guillermo |
| Author_xml | – sequence: 1 givenname: Guillermo orcidid: 0000-0002-2278-6070 surname: Navas-Palencia fullname: Navas-Palencia, Guillermo email: g.navas.palencia@gmail.com organization: Department of Computer Science, Universitat Politècnica de Catalunya, Numerical Algorithms Group Ltd |
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| CitedBy_id | crossref_primary_10_1109_TCOMM_2019_2904499 crossref_primary_10_1007_s10444_017_9565_5 crossref_primary_10_1007_s10712_024_09830_2 crossref_primary_10_1016_j_jhydrol_2024_131995 crossref_primary_10_3847_1538_4365_ac5cb7 crossref_primary_10_1109_TAES_2019_2949395 |
| Cites_doi | 10.1093/imamat/49.3.203 10.1016/0898-1221(87)90134-9 10.1016/0898-1221(90)90098-5 10.1007/BF01397083 10.1007/s101070100263 10.1145/2972951 10.1137/07068031X 10.1112/plms/s2-17.1.116 10.1115/1.2822701 10.1016/0377-0427(91)90181-I 10.1145/2576802.2576828 10.1016/0898-1221(92)90065-P 10.6028/jres.062.022 10.1007/BF02250638 10.1109/ARITH.2001.930115 10.1137/1.9780898717822 10.1137/120872553 |
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| Snippet | We describe an algorithm for the numerical evaluation of the generalized exponential integral
E
ν
(
x
) for positive values of
ν
and
x
. A detailed description... We describe an algorithm for the numerical evaluation of the generalized exponential integral Eν(x) for positive values of ν and x. A detailed description of... |
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| Title | Fast and accurate algorithm for the generalized exponential integral Eν(x) for positive real order |
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