The sign regularity of the auxiliary family gi( x) = xαi(−ln x) βi in convergence acceleration processes using the E-algorithm
The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error...
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| Published in | Journal of computational and applied mathematics Vol. 67; no. 2; pp. 237 - 253 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
01.03.1996
Elsevier |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0377-0427 1879-1778 |
| DOI | 10.1016/0377-0427(95)00016-X |
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| Abstract | The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family
h
n
α
i
(−ln
h
n
)
β
i
(where
h
n
designates the stepsize of the discretization method). |
|---|---|
| AbstractList | The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective error expansion satisfies a certain asymptotic determinantal condition. In this work it is proved that such condition is fulfilled for any error expansion in which formation enter the auxiliary family
h
n
α
i
(−ln
h
n
)
β
i
(where
h
n
designates the stepsize of the discretization method). |
| Author | Graça, Mário M. |
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| Keywords | Sign regularity Error expansion E-algorithm Convergence acceleration Algorithms Error analysis Discretization Numerical solution Numerical methods Differential equations Discretization method |
| Language | English |
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| References | Hȧvie (BIB4) 1979; 19 Brezinski (BIB1) 1980; 35 Wolfram (BIB9) 1991 Lima (BIB6) 1994; 50 Lima, Graça (BIB7) 1995; 61 Brezinski (BIB2) 1982; 8 Brezinski, Redivo Zaglia (BIB3) 1991 Karlin (BIB5) 1968; Vol. I Matos, Prévost (BIB8) 1992; 2 Karlin (10.1016/0377-0427(95)00016-X_BIB5) 1968; Vol. I Lima (10.1016/0377-0427(95)00016-X_BIB7) 1995; 61 Lima (10.1016/0377-0427(95)00016-X_BIB6) 1994; 50 Matos (10.1016/0377-0427(95)00016-X_BIB8) 1992; 2 Brezinski (10.1016/0377-0427(95)00016-X_BIB3) 1991 Brezinski (10.1016/0377-0427(95)00016-X_BIB2) 1982; 8 Hȧvie (10.1016/0377-0427(95)00016-X_BIB4) 1979; 19 Wolfram (10.1016/0377-0427(95)00016-X_BIB9) 1991 Brezinski (10.1016/0377-0427(95)00016-X_BIB1) 1980; 35 |
| References_xml | – volume: 35 start-page: 175 year: 1980 end-page: 187 ident: BIB1 article-title: A general extrapolation algorithm publication-title: Numer. Math. – volume: 50 start-page: 385 year: 1994 end-page: 400 ident: BIB6 article-title: Richardson extrapolation in boundary value problems for differential equations with non-regular right-hand side publication-title: J. Comput. Appl. Math. – year: 1991 ident: BIB9 article-title: Mathematica, a System for Doing Mathematics by Computer – year: 1991 ident: BIB3 article-title: Extrapolation Methods Theory and Practice – volume: 61 start-page: 139 year: 1995 end-page: 164 ident: BIB7 article-title: Convergence acceleration for boundary value problems with singularities using the E-algorithm publication-title: J. Comput. Appl. Math. – volume: Vol. I year: 1968 ident: BIB5 publication-title: Total Positivity – volume: 19 start-page: 204 year: 1979 end-page: 213 ident: BIB4 article-title: Generalized Neville type extrapolation schemes publication-title: BIT – volume: 2 start-page: 393 year: 1992 end-page: 408 ident: BIB8 article-title: Acceleration property for the columns of the E-algorithm publication-title: Numer. Alg. – volume: 8 start-page: 290 year: 1982 end-page: 301 ident: BIB2 article-title: Algorithm 585. A subroutine for the general interpolation and extrapolation problems publication-title: ACM Trans. Math. Software – volume: 35 start-page: 175 year: 1980 ident: 10.1016/0377-0427(95)00016-X_BIB1 article-title: A general extrapolation algorithm publication-title: Numer. Math. doi: 10.1007/BF01396314 – volume: 61 start-page: 139 year: 1995 ident: 10.1016/0377-0427(95)00016-X_BIB7 article-title: Convergence acceleration for boundary value problems with singularities using the E-algorithm publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(94)00065-9 – volume: Vol. I year: 1968 ident: 10.1016/0377-0427(95)00016-X_BIB5 – year: 1991 ident: 10.1016/0377-0427(95)00016-X_BIB3 – year: 1991 ident: 10.1016/0377-0427(95)00016-X_BIB9 – volume: 2 start-page: 393 year: 1992 ident: 10.1016/0377-0427(95)00016-X_BIB8 article-title: Acceleration property for the columns of the E-algorithm publication-title: Numer. Alg. doi: 10.1007/BF02139476 – volume: 19 start-page: 204 year: 1979 ident: 10.1016/0377-0427(95)00016-X_BIB4 article-title: Generalized Neville type extrapolation schemes publication-title: BIT doi: 10.1007/BF01930850 – volume: 8 start-page: 290 year: 1982 ident: 10.1016/0377-0427(95)00016-X_BIB2 article-title: Algorithm 585. A subroutine for the general interpolation and extrapolation problems publication-title: ACM Trans. Math. Software doi: 10.1145/356004.356008 – volume: 50 start-page: 385 year: 1994 ident: 10.1016/0377-0427(95)00016-X_BIB6 article-title: Richardson extrapolation in boundary value problems for differential equations with non-regular right-hand side publication-title: J. Comput. Appl. Math. doi: 10.1016/0377-0427(94)90315-8 |
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| Snippet | The E-algorithm can be successfully applied to accelerate the convergence of the solution of some numerical differential equations provided the respective... |
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| SubjectTerms | Acceleration of convergence Convergence acceleration E-algorithm Error expansion Exact sciences and technology Mathematics Numerical analysis Numerical analysis. Scientific computation Ordinary differential equations Sciences and techniques of general use Sign regularity |
| Title | The sign regularity of the auxiliary family gi( x) = xαi(−ln x) βi in convergence acceleration processes using the E-algorithm |
| URI | https://dx.doi.org/10.1016/0377-0427(95)00016-X |
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