共查询到20条相似文献,搜索用时 15 毫秒
1.
We consider the computation of stable approximations to the exact solution of nonlinear ill-posed inverse problems F(x) = y with nonlinear operators F : X → Y between two Hilbert spaces X and Y by the Newton type methods
in the case that only available data is a noise of y satisfying with a given small noise level . We terminate the iteration by the discrepancy principle in which the stopping index is determined as the first integer such that
with a given number τ > 1. Under certain conditions on {α
k
}, {g
α
} and F, we prove that converges to as and establish various order optimal convergence rate results. It is remarkable that we even can show the order optimality
under merely the Lipschitz condition on the Fréchet derivative F′ of F if is smooth enough. 相似文献
2.
In this paper, the class of nonspreading mappings in Banach spaces is introduced. This class contains the recently introduced
class of firmly nonexpansive type mappings in Banach spaces and the class of firmly nonexpansive mappings in Hilbert spaces.
Among other things, we obtain a fixed point theorem for a single nonspreading mapping in Banach spaces. Using this result,
we also obtain a common fixed point theorem for a commutative family of nonspreading mappings in Banach spaces.
Received: 10 August 2007 相似文献
3.
Feng Gu 《Positivity》2008,12(3):503-509
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend some recent results in Chang
[1], Cho et al. [2] Ofoedu [5], Schu [7] and Zeng [8, 9].
The present studies were supported by “the Natural Science Foundation of China (No. 10771141),” the Natural Science Foundation
of Zhejiang Province (Y605191), the Natural Science Foundation of Heilongjiang Province (A0211), the Scientific Research Foundation
from Zhejiang Province Education Committee (20051897). 相似文献
4.
Koji Aoyama Fumiaki Kohsaka Wataru Takahashi 《Journal of Fixed Point Theory and Applications》2009,5(2):201-225
We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties.
Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive
mappings in a uniformly convex and uniformly smooth Banach space.
相似文献
5.
Let H be a Hilbert space and A, B: H ⇉ H two maximal monotone operators. In this paper, we investigate the properties of the following proximal type algorithm:
where (λ
n
) is a sequence of positive steps. Algorithm may be viewed as the discretized equation of a nonlinear oscillator subject to friction. We prove that, if 0 ∈ int (A(0)) (condition of dry friction), then the sequence (x
n
) generated by is strongly convergent and its limit x
∞ satisfies 0 ∈ A(0) + B(x
∞). We show that, under a general condition, the limit x
∞ is achieved in a finite number of iterations. When this condition is not satisfied, we prove in a rather large setting that
the convergence rate is at least geometrical. 相似文献
6.
7.
We prove convergence for the basic LR algorithm on a real unreduced tridiagonal matrix with a one-point spectrum—the Jordan
form is one big Jordan block. First we develop properties of eigenvector matrices. We also show how to deal with the singular
case. 相似文献
8.
Tomonari Suzuki 《Archiv der Mathematik》2009,92(6):602-613
We discuss Halpern’s convergence for nonexpansive mappings in Hilbert spaces. We prove that one of the conditions in [R. Wittmann,
Approximation of fixed points of nonexpansive mappings, Arch. Math. (Basel), 58 (1992), 486–491] is the weakest sufficient
condition among the conditions known to us. We also improve a necessary condition, which is close to Wittmann’s. This is one
step to solve the problem raised by Reich in 1974 and 1983.
Received: 15 July 2008 相似文献
9.
It was once conjectured that if A is a uniform algebra on its maximal ideal space X, and if each point of X is a peak point for A, then A = C(X). This peak point conjecture was disproved by Brian Cole in 1968. However, Anderson and Izzo showed that the peak point conjecture
does hold for uniform algebras generated by smooth functions on smooth two-manifolds with boundary. The corresponding assertion
for smooth three-manifolds is false, but Anderson, Izzo, and Wermer established a peak point theorem for polynomial approximation
on real-analytic three-manifolds with boundary. Here we establish a more general peak point theorem for real-analytic three-manifolds
with boundary analogous to the two-dimensional result. We also show that if A is a counterexample to the peak point conjecture generated by smooth functions on a manifold of arbitrary dimension, then
the essential set for A has empty interior. 相似文献
10.
Jarosaw Górnicki 《Rendiconti del Circolo Matematico di Palermo》1997,46(1):89-118
In this paper we study in Banach spaces the existence of fixed points of (nonlinear) asymptotically regular semigroups. We
establish for these semigroups some fixed point theorems in spaces with weak uniform normal structure, in a Hilbert space,
inL
p
spaces, in Hardy spacesH
p
and in Sobolev spacesW
r.p
for 1<p<∞ andr≥0, in spaces with Lifshitz’s constant greater than one. These results are the generalizations of [8, 10, 16]. 相似文献
11.
Let f be a nonconstant mapping of finite distortion. We establish integrability results on 1/Jf by studying weights that satisfy a weak reverse Hölder inequality where the associated constant can depend on the ball in question. Here Jf is the Jacobian determinant of f. 相似文献
12.
In this note, we study the non-linear evolution problem $dY_t = -A Y_t dt + B(Y_t) dX_t,$ where $XIn this note, we study the non-linear evolution problem
where is a -H?lder continuous function of the time parameter, with values in a distribution space, and the generator of an analytical semigroup. Then, we will give some sharp conditions on in order to solve the above equation in a function space, first in the linear case (for any value of in ), and then when satisfies some Lipschitz type conditions (for ). The solution of the evolution problem will be understood in the mild sense, and the integrals involved in that definition will be of Young type. 相似文献
13.
In this paper, we present a posteriori error analysis for the nonconforming Morley element of the fourth order elliptic equation.
We propose a new residual-based a posteriori error estimator and prove its reliability and efficiency. These results refine
those of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) by dropping two edge jump terms in both the energy norm of
the error and the estimator, and those of Wang and Zhang (Local a priori and a posteriori error estimates of finite elements
for biharmonic equation, Research Report, 13, 2006) by showing the efficiency in the sense of Verfürth (A review of a posteriori
error estimation and adaptive mesh-refinement techniques, Wiley-Teubner, New York, 1996). Moreover, the normal component in
the estimators of Beirao da Veiga et al. (Numer Math 106:165–179, 2007) and Wang and Zhang (Local a priori and a posteriori
error estimates of finite elements for biharmonic equation, Research Report, 13, 2006) is dropped, and therefore only the
tangential component of the stress on each edge comes into the estimator. In addition, we generalize these results to three
dimensional case. 相似文献
14.
Klaus Thomsen 《Mathematische Annalen》2008,342(2):273-277
It is shown that an extension of the reduced group C
*-algebra of a free group by the compact operators can be made asymptotically split by addition of another extension which
admits a completely positive lifting. 相似文献
15.
The Generalized Minimal Residual method (GMRES) is often used to solve a nonsymmetric linear system Ax = b. But its convergence analysis is a rather difficult task in general. A commonly used approach is to diagonalize A = XΛ X
−1 and then separate the study of GMRES convergence behavior into optimizing the condition number of X and a polynomial minimization problem over A’s spectrum. This artificial separation could greatly overestimate GMRES residuals and likely yields error bounds that are
too far from the actual ones. On the other hand, considering the effects of both A’s spectrum and the conditioning of X at the same time poses a difficult challenge, perhaps impossible to deal with in general but only possible for certain particular
linear systems. This paper will do so for a (nonsymmetric) tridiagonal Toeplitz system. Sharp error bounds on and sometimes
exact expressions for residuals are obtained. These expressions and/or bounds are in terms of the three parameters that define
A and Chebyshev polynomials of the first kind. 相似文献
16.
Markus Haase 《Journal of Evolution Equations》2007,7(3):529-554
Let –iA be the generator of a C
0-group U on a Banach space X. Via a transference principle we obtain results of the form
for certain functions f, provided that X is a UMD space. Special examples are
The first choice leads to easy proofs of the theorems of Monniaux and Dore–Venni, the second is related to a new proof of
Fattorini’s theorem on cosine functions. 相似文献
17.
Aleksander Ćwiszewski 《Journal of Evolution Equations》2007,7(1):1-33
In the paper a topological degree is constructed for the class of maps of the form − A + F where M is a closed neighborhood retract in a Banach space
is a m-accretive map such that − A generates a compact semigroup and F : M→ E is a locally Lipschitz map. The obtained degree is applied to studying the existence and branching of periodic points of
differential inclusions of the type
相似文献
18.
N. M. Ivochkina 《Journal of Fixed Point Theory and Applications》2008,4(1):47-56
We adapt to degenerate m-Hessian evolution equations the notion of m-approximate solutions introduced by N. Trudinger for m-Hessian elliptic equations, and we present close to necessary and sufficient conditions guaranteeing the existence and uniqueness
of such solutions for the first initial boundary value problem.
Dedicated to Professor Felix Browder 相似文献
19.
The purpose of this paper is to introduce a general iterative algorithm by viscosity method to approximate a common point
of a finite family of m-accretive mappings in a reflexive Banach space which has a weakly continuous duality mapping. We obtain strong convergence
theorems under some mild conditions imposed on parameters.
相似文献
20.
Hyoung Joon Kim 《Integral Equations and Operator Theory》2008,61(1):103-120
In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators. Let denote the class of quasinilpotent quasiaffinities Q in such that Q
*
Q has an infinite dimensional reducing subspace M with Q
*
Q|
M
compact. It was known that if every quasinilpotent operator in has a nontrivial hyperinvariant subspace, then every quasinilpotent operator has a nontrivial hyperinvariant subspace. Thus
it suffices to solve the hyperinvariant subspace problem for elements in . The purpose of this paper is to provide sufficient conditions for elements in to have nontrivial hyperinvariant subspaces. We also introduce the notion of “stability” of extremal vectors to give partial
solutions to the hyperinvariant subspace problem.
相似文献