Invariants associated with the epsilon algorithm and its first confluent form

1972 ◽  
Vol 21 (1-2) ◽  
pp. 31-41 ◽  
Author(s):  
P. Wynn
Keyword(s):  
Confluent Form ◽  
Epsilon Algorithm

Unusual Superficial Confluent Form of Granular Corneal Dystrophy

Ophthalmology ◽  
1983 ◽  
Vol 90 (12) ◽  
pp. 1507-1511 ◽  
Author(s):  
Merlyn M. Rodrigues ◽  
Ronald N. Gaster ◽  
Mary V. Pratt
Keyword(s):  
Corneal Dystrophy ◽  
Confluent Form ◽  
Granular Corneal Dystrophy

An Error Compensation Method for Structural Responses and Sensitivities

2011 ◽  
Vol 421 ◽  
pp. 743-749
Author(s):  
Xiao Ming Wu ◽  
Chun Liu
Keyword(s):  
Error Compensation ◽  
Truncation Error ◽  
Compensation Method ◽  
Superposition Method ◽  
Truncation Errors ◽  
Modal Superposition ◽  
Modal Superposition Method ◽  
Structural Responses ◽  
Epsilon Algorithm ◽  
Modal Method

Abstract. The computation of the responses and their design sensitivities play an essential role in structural analysis and optimization. Significant works have been done in this area. Modal method is one of the classical methods. In this study, a new error compensation method is constructed, in which the modal superposition method is hybrid with Epsilon algorithm for responses and their sensitivities analysis of undamped system. In this study the truncation error of modal superposition is expressed by the first L orders eigenvalues and its eigenvectors explicitly. The epsilon algorithm is used to accelerate the convergence of the truncation errors. Numerical examples show that the present method is validity and effectiveness.

Applications of Wynn's epsilon-algorithm to transonic flow-calculations

1987 ◽  
Author(s):  
M. HAFEZ ◽  
S. PALANISWAMY ◽  
G. KURUVILA ◽  
M. SALAS
Keyword(s):  
Transonic Flow ◽  
Epsilon Algorithm

Eigensolution reanalysis of modified structures using epsilon-algorithm

2006 ◽  
Vol 66 (13) ◽  
pp. 2115-2130 ◽  
Author(s):  
Su Huan Chen ◽  
Xiao Ming Wu ◽  
Zhi Jun Yang
Keyword(s):  
Epsilon Algorithm

Static Displacement Reanalysis of Modified Structures Using Epsilon Algorithm

AIAA Journal ◽  
2007 ◽  
Vol 45 (8) ◽  
pp. 2083-2086 ◽  
Author(s):  
Xiao Ming Wu ◽  
Su Huan Chen ◽  
Zhi Jun Yang
Keyword(s):  
Static Displacement ◽  
Epsilon Algorithm

scholarly journals Application of Wynn's epsilon algorithm to periodic continued fractions

1987 ◽  
Vol 30 (2) ◽  
pp. 295-299 ◽  
Author(s):  
M. J. Jamieson
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Rational Numbers ◽  
Quadratic Surd ◽  
Partial Quotients ◽  
Infinite Continued Fraction ◽  
Image Position ◽  
Epsilon Algorithm ◽  
Periodic Continued Fractions

The infinite continued fractionin whichis periodic with period l and is equal to a quadratic surd if and only if the partial quotients, ak, are integers or rational numbers [1]. We shall also assume that they are positive. The transformation discussed below applies only to pure periodic fractions where n is zero.

Acceleration of the EM algorithm using the vector epsilon algorithm

2007 ◽  
Vol 23 (3) ◽  
pp. 469-486 ◽  
Author(s):  
Mingfeng Wang ◽  
Masahiro Kuroda ◽  
Michio Sakakihara ◽  
Zhi Geng
Keyword(s):  
Em Algorithm ◽  
The Em Algorithm ◽  
Epsilon Algorithm

A Local Fractional Taylor Expansion and Its Computation for Insufficiently Smooth Functions

2015 ◽  
Vol 5 (2) ◽  
pp. 176-191 ◽  
Author(s):  
Zhifang Liu ◽  
Tongke Wang ◽  
Guanghua Gao
Keyword(s):  
Theoretical Analysis ◽  
Taylor Expansion ◽  
Fractional Derivatives ◽  
Richardson Extrapolation ◽  
Taylor Formula ◽  
Regular Pattern ◽  
Smooth Functions ◽  
Numerical Examples ◽  
Richardson Extrapolation Method ◽  
Epsilon Algorithm

AbstractA general fractional Taylor formula and its computation for insufficiently smooth functions are discussed. The Aitken delta square method and epsilon algorithm are implemented to compute the critical orders of the local fractional derivatives, from which more critical orders are recovered by analysing the regular pattern of the fractional Taylor formula. The Richardson extrapolation method is used to calculate the local fractional derivatives with critical orders. Numerical examples are provided to verify the theoretical analysis and the effectiveness of our approach.

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