Norm-Preserving Dilations and Their Applications to Optimal Error Bounds

1982 ◽  
Vol 19 (3) ◽  
pp. 445-469 ◽  
Author(s):  
Chandler Davis ◽  
W. M. Kahan ◽  
H. F. Weinberger
Keyword(s):  
Error Bounds ◽  
Optimal Error

scholarly journals Revisited Optimal Error Bounds for Interpolatory Integration Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
François Dubeau
Keyword(s):  
Error Bounds ◽  
Error Term ◽  
Quadrature Rules ◽  
Optimal Error ◽  
Integration By Parts ◽  
Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

scholarly journals Optimal error bounds for two-grid schemes applied to the Navier–Stokes equations

2012 ◽  
Vol 218 (13) ◽  
pp. 7034-7051 ◽  
Author(s):  
Javier de Frutos ◽  
Bosco García-Archilla ◽  
Julia Novo
Keyword(s):  
Error Bounds ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Optimal Error ◽  
Navier Stokes Equations

scholarly journals Optimal Error Bounds for Convergents of a Family of Continued Fractions

1996 ◽  
Vol 197 (3) ◽  
pp. 767-773 ◽  
Author(s):  
Yair Shapira ◽  
Avram Sidi ◽  
Moshe Israeli
Keyword(s):  
Error Bounds ◽  
Continued Fractions ◽  
Optimal Error

scholarly journals ON THE INF–SUP CONDITION OF MIXED FINITE ELEMENT FORMULATIONS FOR ACOUSTIC FLUIDS

2001 ◽  
Vol 11 (05) ◽  
pp. 883-901 ◽  
Author(s):  
WEIZHU BAO ◽  
XIAODONG WANG ◽  
KLAUS-JÜRGEN BATHE
Keyword(s):  
Finite Element ◽  
Error Bounds ◽  
Natural Frequencies ◽  
Mixed Finite Element ◽  
Optimal Error ◽  
Finite Element Discretizations ◽  
Analytical Proof ◽  
The Stability ◽  
Element Discretizations ◽  
Finite Element Formulations

The objective of this paper is to present a study of the solvability, stability and optimal error bounds of certain mixed finite element formulations for acoustic fluids. An analytical proof of the stability and optimal error bounds of a set of three-field mixed finite element discretizations is given, and the interrelationship between the inf–sup condition, including the numerical inf–sup test, and the eigenvalue problem pertaining to the natural frequencies is discussed.

scholarly journals Asymptotics of Landau Constants with Optimal Error Bounds

2014 ◽  
Vol 40 (2) ◽  
pp. 281-305 ◽  
Author(s):  
Yutian Li ◽  
Saiyu Liu ◽  
Shuaixia Xu ◽  
Yuqiu Zhao
Keyword(s):  
Error Bounds ◽  
Optimal Error

Convergence Rates For Lavrentiev-Type Regularization In Hilbert Scales

2008 ◽  
Vol 8 (3) ◽  
pp. 279-293 ◽  
Author(s):  
M.T. NAIR ◽  
U. TAUTENHAHN
Keyword(s):  
Error Bounds ◽  
Convergence Rates ◽  
Noisy Data ◽  
Regularization Methods ◽  
Operator Equations ◽  
Optimal Error ◽  
Regularization Scheme ◽  
Data Regularization ◽  
Ill Posed ◽  
Adjoint Operators

AbstractFor solving linear ill-posed problems with noisy data regularization methods are required. We analyze a simplified regularization scheme in Hilbert scales for operator equations with nonnegative self-adjoint operators. By exploiting the op-erator monotonicity of certain functions, order-optimal error bounds are derived that characterize the accuracy of the regularized approximations. These error bounds have been obtained under general smoothness conditions.

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