A VARIATIONAL CHARACTERIZATION OF THE BEST APPROXIMATION ELEMENT

1999 ◽  
Vol 32 (1) ◽  
Author(s):  
Sever Silvestru Dragomir
Keyword(s):  
Best Approximation ◽  
Variational Characterization ◽  
The Best Approximation ◽  
Approximation Element ◽  
Best Approximation Element

scholarly journals Lagrange multiplier characterizations of constrained best approximation with nonsmooth nonconvex constraints

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4669-4684
Author(s):  
H. Mohebi
Keyword(s):  
Lagrange Multiplier ◽  
Best Approximation ◽  
Constraint Qualification ◽  
Sufficient Conditions ◽  
Dual Cone ◽  
The Best Approximation ◽  
Constraint Set ◽  
Nonconvex Constraint ◽  
Constrained Best Approximation

In this paper, we consider the constraint set K := {x ? Rn : gj(x)? 0,? j = 1,2,...,m} of inequalities with nonsmooth nonconvex constraint functions gj : Rn ? R (j = 1,2,...,m).We show that under Abadie?s constraint qualification the ?perturbation property? of the best approximation to any x in Rn from a convex set ?K := C ? K is characterized by the strong conical hull intersection property (strong CHIP) of C and K, where C is an arbitrary non-empty closed convex subset of Rn: By using the idea of tangential subdifferential and a non-smooth version of Abadie?s constraint qualification, we do this by first proving a dual cone characterization of the constraint set K. Moreover, we present sufficient conditions for which the strong CHIP property holds. In particular, when the set ?K is closed and convex, we show that the Lagrange multiplier characterizations of constrained best approximation holds under a non-smooth version of Abadie?s constraint qualification. The obtained results extend many corresponding results in the context of constrained best approximation. Several examples are provided to clarify the results.

scholarly journals Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

2021 ◽  
Vol 13 (3) ◽  
pp. 750-763
Author(s):  
Z. Cakir ◽  
C. Aykol ◽  
V.S. Guliyev ◽  
A. Serbetci
Keyword(s):  
Best Approximation ◽  
Variable Exponent ◽  
Modulus Of Smoothness ◽  
Morrey Spaces ◽  
Trigonometric Polynomials ◽  
The Best Approximation ◽  
Weighted Morrey Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.

scholarly journals On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Devendra Kumar
Keyword(s):  
Rational Approximation ◽  
Analytic Functions ◽  
Best Approximation ◽  
Maximum Modulus ◽  
Approximation Of Functions ◽  
The Best Approximation ◽  
Approximation Errors ◽  
Rate Of Decay ◽  
Rates Of Growth

The present paper is concerned with the rational approximation of functions holomorphic on a domainG⊂C, having generalized types of rates of growth. Moreover, we obtain the characterization of the rate of decay of product of the best approximation errors for functionsfhaving fast and slow rates of growth of the maximum modulus.

A new method for approximation of closed convex subsets of B(H)

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6005-6013
Author(s):  
Mahdi Iranmanesh ◽  
Fatemeh Soleimany
Keyword(s):  
Best Approximation ◽  
Numerical Range ◽  
New Method ◽  
C Algebra ◽  
Convex Subsets

In this paper we use the concept of numerical range to characterize best approximation points in closed convex subsets of B(H): Finally by using this method we give also a useful characterization of best approximation in closed convex subsets of a C*-algebra A.

Intracranial volume-pressure relationship in man

1982 ◽  
Vol 56 (4) ◽  
pp. 524-528 ◽  
Author(s):  
Joseph Th. J. Tans ◽  
Dick C. J. Poortvliet
Keyword(s):  
Best Approximation ◽  
Continuous Monitoring ◽  
Fluid Pressure ◽  
Constant Term ◽  
Volume Index ◽  
Intracranial Volume ◽  
Content Type ◽  
The Best Approximation ◽  
Ventricular Fluid Pressure ◽  
Fine Print

✓ The pressure-volume index (PVI) was determined in 40 patients who underwent continuous monitoring of ventricular fluid pressure. The PVI value was calculated using different mathematical models. From the differences between these values, it is concluded that a monoexponential relationship with a constant term provides the best approximation of the PVI.

Variational characterization of real eigenvalues in linear viscoelastic oscillators

2017 ◽  
Vol 23 (10) ◽  
pp. 1377-1388 ◽  
Author(s):  
Seyyed Abbas Mohammadi ◽  
Heinrich Voss
Keyword(s):  
Degrees Of Freedom ◽  
Nonlinear Eigenvalue Problem ◽  
Eigenvalues And Eigenvectors ◽  
Variational Characterization ◽  
Viscoelastic System ◽  
New Approach ◽  
Motion Equations ◽  
Multiple Degrees Of Freedom ◽  
Linear Viscoelastic

This paper proposes a new approach for computing the real eigenvalues of a multiple-degrees-of-freedom viscoelastic system in which we assume an exponentially decaying damping. The free-motion equations lead to a nonlinear eigenvalue problem. If the system matrices are symmetric, the eigenvalues allow for a variational characterization of maxmin type, and the eigenvalues and eigenvectors can be determined very efficiently by the safeguarded iteration, which converges quadratically and, for extreme eigenvalues, monotonically. Numerical methods demonstrate the performance and the reliability of the approach. The method succeeds where some current approaches, with restrictive physical assumptions, fail.

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