4th degree algebraic hermite-padé approximation to the exponential function

4th Degree algebraic Hermite-Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas and differential equations are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and...

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Bibliographic Details
Published in:International journal of computer mathematics 2004-01, Vol.81 (1), p.35-48
Main Authors: Zheng, C.-D., Ren-hong, W
Format: Article
Language:English
Subjects:
Asymptotic formula
Cubic Hermite-Padé approximation
Differential equation
Padé-type approximant
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Summary:4th Degree algebraic Hermite-Padé approximation to the exponential function with coefficient polynomials of degree at most m is considered. Explicit formulas and differential equations are obtained for the coefficient polynomials. An exact asymptotic expression is obtained for the error function and it is also shown that these generalized Padé-type approximations can be used to asymptotically minimize the expressions on the unit disk. * The work is supported by The National Natural Science Foundation of China (Nos 69973010 and 10271022) and The Guangdong Natural Science Foundation of Guangdong Province, China (No. 021755).
ISSN:0020-7160
1029-0265
DOI:10.1080/0020716031000148160