Hermite–Birkhoff Interpolation Polynomial of Minimum Norm in Hilbert Space

2021 ◽  
Author(s):  
O. F. Kashpur
Keyword(s):  
Hilbert Space ◽  
Interpolation Polynomial ◽  
Minimum Norm ◽  
Birkhoff Interpolation

INERTIAL RELAXED TSENG METHOD FOR SOLVING VARIATIONAL INEQUALITY PROBLEM IN HILBERT SPACE

2021 ◽  
Vol 10 (12) ◽  
pp. 3597-3623
Author(s):  
F. Akusah ◽  
A.A. Mebawondu ◽  
H.A. Abass ◽  
M.O. Aibinu ◽  
O.K. Narain
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Numerical Experiments ◽  
Variational Inequality Problem ◽  
Extrapolation Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Inequality Problem ◽  
Weaker Conditions

The research efforts of this paper is to present a new inertial relaxed Tseng extrapolation method with weaker conditions for approximating the solution of a variational inequality problem, where the underlying operator is only required to be pseudomonotone. The strongly pseudomonotonicity and inverse strongly monotonicity assumptions which the existing literature used are successfully weakened. The strong convergence of the proposed method to a minimum-norm solution of a variational inequality problem are established. Furthermore, we present an application and some numerical experiments to show the efficiency and applicability of our method in comparison with other methods in the literature.

scholarly journals Strong Convergence of a Modified Extragradient Method to the Minimum-Norm Solution of Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yonghong Yao ◽  
Muhammad Aslam Noor ◽  
Yeong-Cheng Liou
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Extragradient Method ◽  
Minimum Norm ◽  
Minimum Norm Solution ◽  
Infinite Dimensional ◽  
Infinite Dimensional Hilbert Space ◽  
Dimensional Hilbert Space

We suggest and analyze a modified extragradient method for solving variational inequalities, which is convergent strongly to the minimum-norm solution of some variational inequality in an infinite-dimensional Hilbert space.

scholarly journals STRONG CONVERGENCE OF SOME ALGORITHMS FOR λ-STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACE

2012 ◽  
Vol 85 (2) ◽  
pp. 232-240 ◽  
Author(s):  
YONGHONG YAO ◽  
YEONG-CHENG LIOU ◽  
GIUSEPPE MARINO
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Minimum Norm

AbstractTwo algorithms have been constructed for finding the minimum-norm fixed point of a λ-strict pseudo-contraction T in Hilbert space. It is shown that the proposed algorithms strongly converge to the minimum-norm fixed point of T.

scholarly journals Perturbation bounds for the Moore-Penrose inverse of operators

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 353-362
Author(s):  
Xiaoji Liu ◽  
Yonghui Qin ◽  
Dragana Cvetkovic-Ilic
Keyword(s):  
Hilbert Space ◽  
Least Squares ◽  
Minimum Norm ◽  
Perturbation Bounds ◽  
Least Squares Solution ◽  
Relative Errors

We consider the perturbation bounds for the Moore-Penrose inverse of a given operator on Hilbert space and apply these results to the relative errors of the minimum norm least squares solution of the equation Ax = b.

The Analytic Character of the Birkhoff Interpolation Polynomials

1982 ◽  
Vol 34 (3) ◽  
pp. 765-768
Author(s):  
G. G. Lorentz
Keyword(s):  
Entire Function ◽  
Hermite Interpolation ◽  
Interpolation Polynomial ◽  
Birkhoff Interpolation ◽  
Interpolation Matrix ◽  
Image Position ◽  
Interpolation Polynomials

Let E be an m × (n + 1) regular interpolation matrix with elements ei, k = (E)i, k which are zero or one, with n + 1 ones. Then for each f ∈ Cn[a, b] and each set of knots X: a ≦ x1 < … < xm ≦ b, there is a unique interpolation polynomial P(f, E, X; t) of degree ≦ n which satisfies1A recent paper [1] discussed the continuity of P, as a function of x1, …,xm(with coalescences allowed). We would like to study in this note the analytic character of P as a function of real or complex knots X: x1, …, xm. This is easy for the Lagrange or the Hermite interpolation. In this case P is a polynomial in x1, …, xm if f is a polynomial, and an entire function in x1, …, xm if f is entire.

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