共查询到19条相似文献,搜索用时 734 毫秒
1.
讨论了Clifford分析中一个带超正则函数核的Cauchy型算子和T型算子的性质,并且利用压缩不动点原理证明了一类广义超正则函数向量的线性边值问题解的存在性. 相似文献
2.
求解病态问题的一种改进的Tikhonov正则化:⑴正则化方法的建立 总被引:1,自引:0,他引:1
对于带有右扰动数据的第一类紧算子方程的病态问题。本文应用正则化子建立了一类新的正则化求解方法,称之为改进的Tikonov正则化;通过适当选取2正则参数,证明了正则解具有最优的渐近收敛阶,与通常的Tikhonov正则化相比,这种改进的正则化可使正则解取到足够高的最优渐近阶。 相似文献
3.
该文利用欧拉算子得出了多正则函数边值问题的解, 同时给出了欧拉算子的一些应用. 相似文献
4.
张寄洲 《数学物理学报(A辑)》2005,25(1):27-34
设K∈C(R+)和B是一个有界线性算子.作者证明如果犃生成一个指数有界的A正则预解算子族,那么BA,AB或A(I+B),(I+B)A也生成一个指数有界的k-正则预解算子族.此外,作者也给出了k正则预解算子族的加法扰动的相应结果. 相似文献
5.
对滞右端扰动数据的第一类紧算子病态方程,文[2]给出了改进的Tokhonov正则化解法,本文以此为依据,对该解法举例进行例法分析。 相似文献
6.
该文研究Hilbert空间H上正则射影对(P,Q)的性质和结构,给出H上有界线性算子A表示为两个正交射影乘积的充分必要条件. 相似文献
7.
8.
关于迭代Tikhonov正则化的最优正则参数选取 总被引:2,自引:0,他引:2
本文讨论了算子和右端都近似给定的第一类算子方程的迭代Tikhonov正则化,给出了不依赖于准确解的任何信息但能得到最优收敛阶的正则参数选取法。 相似文献
9.
10.
A—光滑正则化算子 总被引:3,自引:0,他引:3
贺国强 《高校应用数学学报(A辑)》1992,7(4):568-578
本文研究了紧算子方程的Moore-Penrose广义解的逼近,引进了A-导数的概念和对应的A-光滑正则化算子.这个双参数的A-光滑正则化算子族有明显的变分意义,并且包含正则化算子作为它的特殊情形,以(修正的)截断奇异值分解方法作为它的极限情形.这些正则化算子的性质表明它们有广阔的实际应用可能性. 相似文献
11.
In this paper, we establish Desch-Schappacher type multiplicative and additive perturbation theorems for existence families for arbitrary order abstract Cauchy problems in a Banach space: ; . As a consequence, we obtain such perturbation results for regularized semigroups and regularized cosine operator functions. An example is also given to illustrate possible applications.
12.
LetA be a closed linear operator such that the abstract Cauchy problemu″(t)=Au(t), t∈R; u(0)=x, u′(0)=y, is well-posed. We present some multiplicative perturbation theorems which give conditions on an operatorC so that the abstract Cauchy problems for differential equationsu″(t)=ACu(t) andu″(t)=CAu(t) also are well-posed. Some new or known additive perturbation theorems and mixed-type perturbation theorems are deduced as
corollaries. Applications to characterization of the infinitesimal comparison of two cosine operator functions are also discussed.
Research supported in part by the National Science Council of Taiwan. 相似文献
13.
We prove general theorems on mean ergodicity and mean stability
of regularized solution families with respect to fairly general summability
methods. They can be applied to integrated solution families, integrated semigroups
and cosine functions. In particular, through applications with modified
Cesàro, Abel, Gauss, and Gamma like summability methods we deduce particular
results on mean ergodicity and mean stability of polynomially bounded
C0-semigroups and cosine operator functions. 相似文献
14.
D. Lutz 《Periodica Mathematica Hungarica》1983,14(1):101-105
On convergence of operator cosine functions with perturbed infinitesimal generator. The question under what kind of perturbations a closed linear operatorA remains of the class of infinitesimal generators of operator cosine functions seems to be a rather difficult one and is unsolved in general. In this note we give bounds for the perturbation of operator cosine functions caused byA-bounded perturbationsT ofA under the assumption thatT + A is also a generator. 相似文献
15.
George A. Anastassiou 《Semigroup Forum》2008,76(1):149-158
Various L
p
form Opial type inequalities are given for cosine and sine operator functions with applications. 相似文献
16.
The paper contains formulas for regularized traces of the Laplace-Beltrami operator on the unit sphere under perturbation
determined by a bounded complex-valued potential and a sufficiently complete justification of these formulas.
Translated fromMatematicheskie Zametki, Vol. 67, No. 5, pp. 702–705, May, 2000. 相似文献
17.
George A. Anastassiou 《Semigroup Forum》2009,78(1):54-67
Here we present Poincaré type general L
p
inequalities regarding semigroups, cosine and sine operator functions. 相似文献
18.
19.
Li Gongsheng 《Numerical Functional Analysis & Optimization》2013,34(4-5):543-563
We construct with the aid of regularizing filters a new class of improved regularization methods, called modified Tikhonov regularization (MTR), for solving ill-posed linear operator equations. Regularizing properties and asymptotic order of the regularized solutions are analyzed in the presence of noisy data and perturbation error in the operator. With some accurate estimates in the solution errors, optimal convergence order of the regularized solutions is obtained by a priori choice of the regularization parameter. Furthermore, numerical results are given for several ill-posed integral equations, which not only roughly coincide with the theoretical results but also show that MTR can be more accurate than ordinary Tikhonov regularization (OTR). 相似文献