For solving the large-scale linear least-squares problem, we propose a block version of the randomized extended Kaczmarz method, called the two-subspace randomized extended Kaczmarz method, which does not require any row or column paving. Theoretical analysis and numerical results show that the two-subspace randomized extended Kaczmarz method is much more efficient than the randomized extended Kaczmarz method. When the coefficient matrix is of full column rank, the two-subspace randomized extended Kaczmarz method can also outperform the randomized coordinate descent method. If the linear system is consistent, we remove one of the iteration sequences in the two-subspace randomized extended Kaczmarz method, which approximates the projection of the right-hand side vector onto the orthogonal complement space of the range space of the coefficient matrix, and obtain the generalized two-subspace randomized Kaczmarz method, which is actually a generalization of the two-subspace randomized Kaczmarz method without the assumptions of unit row norms and full column rank on the coefficient matrix. We give the upper bound for the convergence rate of the generalized two-subspace randomized Kaczmarz method which also leads to a better upper bound for the convergence rate of the two-subspace randomized Kaczmarz method.
Summary Consider a Markov process on the real line with a specified transition density function. Certain conditions on the latter are shown to be sufficient for the almost sure existence of a local time of the sample function which is jointly continuous in the state and time variables.This paper represents results obtained at the Courant Institute of Mathematical Sciences, New York University, under the sponsorship of the National Science Foundation, Grant MCS 82-01119 相似文献
We present a modification of Dykstra's algorithm which allows us to avoid projections onto general convex sets. Instead, we calculate projections onto either a half-space or onto the intersection of two half-spaces. Convergence of the algorithm is established and special choices of the half-spaces are proposed.The option to project onto half-spaces instead of general convex sets makes the algorithm more practical. The fact that the half-spaces are quite general enables us to apply the algorithm in a variety of cases and to generalize a number of known projection algorithms.The problem of projecting a point onto the intersection of closed convex sets receives considerable attention in many areas of mathematics and physics as well as in other fields of science and engineering such as image reconstruction from projections.In this work we propose a new class of algorithms which allow projection onto certain super half-spaces, i.e., half-spaces which contain the convex sets. Each one of the algorithms that we present gives the user freedom to choose the specific super half-space from a family of such half-spaces. Since projecting a point onto a half-space is an easy task to perform, the new algorithms may be more useful in practical situations in which the construction of the super half-spaces themselves is not too difficult. 相似文献
Let x(t), 0 ≦ t ≦ 1, be a real measurable function having a local time α(x, t) which is a continuous function of t for almost all x. It is also assumed that, for some m ≧ 2 and some real interval B, αm(x, 1) is integrable over B. The modulator is a function Mm(t, B), t > 0, denned in terms of α. It is shown that the modulator serves as a measure of the smoothness of the Lm(B)-valued function α(., t) with respect to t. Then it is shown that the modulator plays a central role in precisely describing certain irregularity properties of x(t). The results are applied to the case where x(t) is the sample function of a real stochastic process. In this way new results are obtained for large classes of Gaussian and Markov processes. 相似文献
The compounds Ae3Sn4?xBi1+x (Ae = Sr, Ba) with x < 1 have been synthesized by solid‐state reactions in welded Nb tubes at high temperature. Their structures were determined by single crystal X‐ray diffraction studies to be tetragonal; space group I4/mcm (No. 140); Z = 4, with a = 8.968(1) Å, c = 12.859(1) Å for Sr3Sn3.36Bi1.64(3) ( 1 ) and a = 9.248(2), c = 13.323(3) Å for Ba3Sn3.16Bi1.84(3) ( 2 ). The structure consists of two interpenetrating networks formed by a 3D Ae6/2Bi substructure (anti‐ReO3 type) forming the host, and layers of interconnected four‐member units [Sn4?xBix] with “butterfly”‐like shape as the guest. According to the Zintl‐Klemm concept, the compounds are slightly electron deficient and will be charge balanced for x = 1. The electronic structures of Ae3Sn4?xBi1+x calculated by the TB‐LMTO‐ASA method indicate that the compounds correspond to ideal semiconducting Zintl phases with a narrow band gap for x = 1 (zero‐gap semiconductor). The origin of the slight deviation from the optimal electron count for a valance compound is discussed. 相似文献
Assuming that the absence of perturbations guarantees weak or strong convergence to a common fixed point, we study the behavior of perturbed products of an infinite family of nonexpansive operators. Our main result indicates that the convergence rate of unperturbed products is essentially preserved in the presence of perturbations. This, in particular, applies to the linear convergence rate of dynamic string-averaging projection methods, which we establish here as well. Moreover, we show how this result can be applied to the superiorization methodology. 相似文献
In this paper, we study the local structure of the fixed point set of a holomorphic mapping defined on a (not necessarily bounded or convex) domain in a complex Banach space, using ergodic theory of linear operators and the nonlinear numerical range introduced by L. A. Harris. We provide several constructions of holomorphic retractions and a generalization of Cartan’s Uniqueness Theorem. We also estimate the deviation of a holomorphic mapping from its linear approximation, the Fréchet derivative at a fixed point. 相似文献