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101.
102.
Circulant preconditioners are commonly used to accelerate the rate of convergence of iterative methods when solving linear systems of equations with a Toeplitz matrix. Block extensions that can be applied when the system has a block Toeplitz matrix with Toeplitz blocks also have been developed. This paper is concerned with preconditioning of linear systems of equations with a symmetric block Toeplitz matrix with symmetric Toeplitz blocks that stem from the discretization of a linear ill-posed problem. The right-hand side of the linear systems represents available data and is assumed to be contaminated by error. These kinds of linear systems arise, e.g., in image deblurring problems. It is important that the preconditioner does not affect the invariant subspace associated with the smallest eigenvalues of the block Toeplitz matrix to avoid severe propagation of the error in the right-hand side. A perturbation result indicates how the dimension of the subspace associated with the smallest eigenvalues should be chosen and allows the determination of a suitable preconditioner when an estimate of the error in the right-hand side is available. This estimate also is used to decide how many iterations to carry out by a minimum residual iterative method. Applications to image restoration are presented. 相似文献
103.
104.
The computation of an approximate solution of linear discrete ill-posed problems with contaminated data is delicate due to
the possibility of severe error propagation. Tikhonov regularization seeks to reduce the sensitivity of the computed solution
to errors in the data by replacing the given ill-posed problem by a nearby problem, whose solution is less sensitive to perturbation.
This regularization method requires that a suitable value of the regularization parameter be chosen. Recently, Brezinski et al.
(Numer Algorithms 49, 2008) described new approaches to estimate the error in approximate solutions of linear systems of equations and applied these
estimates to determine a suitable value of the regularization parameter in Tikhonov regularization when the approximate solution
is computed with the aid of the singular value decomposition. This paper discusses applications of these and related error
estimates to the solution of large-scale ill-posed problems when approximate solutions are computed by Tikhonov regularization
based on partial Lanczos bidiagonalization of the matrix. The connection between partial Lanczos bidiagonalization and Gauss
quadrature is utilized to determine inexpensive bounds for a family of error estimates.
In memory of Gene H. Golub.
This work was supported by MIUR under the PRIN grant no. 2006017542-003 and by the University of Cagliari. 相似文献
105.
Wolfgang Reichel 《Journal of Differential Equations》2010,248(7):1866-680
We consider the 2m-th order elliptic boundary value problem Lu=f(x,u) on a bounded smooth domain Ω⊂RN with Dirichlet boundary conditions on ∂Ω. The operator L is a uniformly elliptic linear operator of order 2m whose principle part is of the form . We assume that f is superlinear at the origin and satisfies , , where are positive functions and q>1 is subcritical. By combining degree theory with new and recently established a priori estimates, we prove the existence of a nontrivial solution. 相似文献
106.
Hans-Christian Graf von Bothmer Kristian Ranestad Frank Sottile 《Foundations of Computational Mathematics》2010,10(1):37-66
We classify the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation.
This classification includes, as a proper subset, the classification of toric surface patches from geometric modeling which
have linear precision. Besides the well-known tensor product patches and Bézier triangles, we identify a family of toric patches
with trapezoidal shape, each of which has linear precision. Furthermore, Bézier triangles and tensor product patches are special
cases of trapezoidal patches. 相似文献
107.
108.
Karlsson S Boixel J Pellegrin Y Blart E Becker HC Odobel F Hammarström L 《Journal of the American Chemical Society》2010,132(51):17977-17979
Molecular systems that follow the functional principles of photosynthesis have attracted increasing attention as a method for the direct production of solar fuels. This could give a major carbon-neutral energy contribution to our future society. An outstanding challenge in this research is to couple the light-induced charge separation (which generates a single electron-hole pair) to the multielectron processes of water oxidation and fuel generation. New design considerations are needed to allow for several cycles of photon absorption and charge separation of a single artificial photosystem. Here we demonstrate a molecular system with a regenerative photosensitizer that shows two successive events of light-induced charge separation, leading to high-yield accumulation of redox equivalents on single components without sacrificial agents. 相似文献
109.
J. Tichý H. Mitsch J. Schoissengeier H. G. Feichtinger H. C. Reichel E. Kotzmann N. Hofreiter H. Rindler J. Hejtmanek H. Muthsam K. Sigmund E. Hlawka 《Monatshefte für Mathematik》1977,84(4):341-347
Ohne Zusammenfassung 相似文献
110.
Wolfgang Reichel 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2003,54(5):822-838
We consider the equation
(pu)-qu+wu
= f
in (0,1) subject to homogenous boundary conditions at
x = 0
and
x = 1, e.g.,
u(0)
= u(1) = 0. Let
1
be the first eigenvalue of the corresponding Sturm-Liouville problem. If
f 0
but
0 then it is known that there exists
> 0 (independent on
f) such that for
(1,
1 + ]
any solution
u
must be negative. This so-called
uniform anti-maximum principle
(UAMP)
goes back to Clément, Peletier [4]. In this paper we
establish the sharp values of
for which (UAMP) holds. The same phenomenon, including sharp values of
, can be shown for the radially symmetric
p-Laplacian on balls and annuli in
n
provided
1 n <
p. The results are illustrated by
explicitly computed examples. 相似文献