共查询到20条相似文献,搜索用时 15 毫秒
1.
Mohammad Masjed-Jamei 《Numerical Functional Analysis & Optimization》2013,34(11):1224-1244
A certain class of weighted approximations, which extends the results of Masjed-Jamei [6] is introduced for integrable functions and some of upper bounds are obtained for the absolute value of the errors of such approximations in two L1[a, b] and L∞[a, b] spaces. As the main motivation for introducing the aforesaid class, it is shown that many new inequalities can be generated from the given error bounds. Some illustrative examples are presented in this sense. Moreover, by using the obtained error bounds, a nonstandard type of three-point weighted quadrature rules is introduced and its error bounds are computed. 相似文献
2.
A perturbation bound for the Drazin inverse AD with Ind(A+E)=1 has recently been developed. However, those upper bounds are not satisfied since it is not tight enough. In this paper, a sharper upper bounds for ||(A+E)#−AD|| with weaker conditions is derived. That new bound is also a generalization of a new general upper bound of the group inverse. We also derive a new expression of the Drazin inverse (A+E)D with Ind(A+E)>1 and the corresponding upper bound of ||(A+E)D−AD|| in a special case. Numerical examples are given to illustrate the sharpness of the new bounds. 相似文献
3.
In this paper, we consider the perturbation of the orthogonal projection and the generalized inverse for an n × n matrix A and present some perturbation bounds for the orthogonal projections on the rang spaces of A and A?, respectively. A combined bound for the orthogonal projection on the rang spaces of A and A? is also given. The proposed bounds are sharper than the existing ones. From the combined bounds of the orthogonal projection on the rang spaces of A and A?, we derived new perturbation bounds for the generalized inverse, which always improve the existing ones. The combined perturbation bound for the orthogonal projection and the generalized inverse is also given. Some numerical examples are given to show the advantage of the new bounds. 相似文献
4.
Wang Fengyu 《数学学报(英文版)》1997,13(1):116-126
By using diffusion process with absorbing boundary, some lower bounds are obtained for the first Dirichlet eigenvalue of operator
Δ+∇h on a non-compact complete Riemannian manifold. The resulting estimates contain McKean's estimate for ∇h=0. Moreover, the first Dirichlet eigenvalue for elliptic operators onR
d
and the first mixed eigenvalue are also studied. Some examples show that our estimates can be sharp even for ∇h≠0.
Research supported in part by NFSC and the State Education Commission of China 相似文献
5.
André Draux 《Numerical Algorithms》2000,24(1-2):31-58
Some methods of numerical analysis, used for obtaining estimations of zeros of polynomials, are studied again, more especially
in the case where the zeros of these polynomials are all strictly positive, distinct and real. They give, in particular, formal
lower and upper bounds for the smallest zero. Thanks to them, we produce new formal lower and upper bounds of the constant
in Markov-Bernstein inequalities in L
2 for the norm corresponding to the Laguerre and Gegenbauer inner products. In fact, since this constant is the inverse of
the square root of the smallest zero of a polynomial, we give formal lower and upper bounds of this zero. Moreover, a new
sufficient condition is given in order that a polynomial has some complex zeros.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
We obtain lower bounds for solutions of some extremal problems on classes of functions W
rH1ω with integral modulus of continuity ω(t). Some of these bounds are regarded as exact.
Dneprodzerzhinsk Technical University, Dneprodzerzhinsk. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No.
11. pp. 1499–1503, November, 1997. 相似文献
7.
Saumya Bajpai Neela Nataraj Amiya K. Pani Pedro Damazio Jin Yun Yuan 《Numerical Methods for Partial Differential Equations》2013,29(3):857-883
Finite element Galerkin method is applied to equations of motion arising in the Kelvin–Voigt model of viscoelastic fluids for spatial discretization. Some new a priori bounds which reflect the exponential decay property are obtained for the exact solution. For optimal L∞( L 2) estimate in the velocity, a new auxiliary operator which is based on a modification of the Stokes operator is introduced and analyzed. Finally, optimal error bounds for the velocity in L∞( L 2) as well as in L∞( H )‐norms and the pressure in L∞(L2)‐norm are derived which again preserves the exponential decay property. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 相似文献
8.
The concept of t-designs in compact symmetric spaces of rank 1 is a generalization of the theory of classical t-designs. In this paper we obtain new lower bounds on the cardinality of designs in projective compact symmetric spaces of rank 1. With one exception our bounds are the first improvements of the classical bounds by more than one. We use the linear programming technique and follow the approach we have proposed for spherical codes and designs. Some examples are shown and compared with the classical bounds. 相似文献
9.
A weighing matrix of order n and weight m2 is a square matrix M of order n with entries from {-1,0,+1} such that MMT=m2I where I is the identity matrix of order n. If M is a group matrix constructed using a group of order n, M is called a group weighing matrix. Recently, group weighing matrices were studied intensively, especially when the groups are cyclic and abelian. In this paper, we study the abelian group weighing matrices that are symmetric, i.e.MT=M. Some new examples are found. Also we obtain a few exponent bounds on abelian groups that admit symmetric group weighing matrices. In particular, we prove that there is no symmetric abelian group weighing matrices of order 2pr and weight p2 where p is a prime and p≥ 5.Communicated by: K.T. Arasu 相似文献
10.
Bo Kågström 《BIT Numerical Mathematics》1977,17(1):39-57
Some new types of bounds and perturbation bounds, based on the Jordan normal form, for the matrix exponential are derived. These bounds are compared to known bounds, both theoretically and by numerical examples. Some recent results on the matrix exponential and the logarithmic norm are also included. 相似文献
11.
The aim is to find the maximum size of a set of mutually ske lines on a nonsingular Hermitian surface in PG(3, q) for various values of q. For q = 9 such extremal sets are intricate combinatorial structures intimately connected ith hemisystems, subreguli, and commuting null polarities. It turns out they are also closely related to the classical quartic surface of Kummer. Some bounds and examples are also given in the general case. 相似文献
12.
A real multivariate polynomial p(x
1, …, x
n
) is said to sign-represent a Boolean function f: {0,1}
n
→{−1,1} if the sign of p(x) equals f(x) for all inputs x∈{0,1}
n
. We give new upper and lower bounds on the degree of polynomials which sign-represent Boolean functions. Our upper bounds
for Boolean formulas yield the first known subexponential time learning algorithms for formulas of superconstant depth. Our lower bounds for constant-depth circuits and intersections of halfspaces are the first new degree lower bounds
since 1968, improving results of Minsky and Papert. The lower bounds are proved constructively; we give explicit dual solutions to the necessary linear programs. 相似文献
13.
In this paper, we study the numerical computation of the errors in linear systems when using iterative methods. This is done
by using methods to obtain bounds or approximations of quadratic formsu
T
A
−1
u whereA is a symmetric positive definite matrix andu is a given vector. Numerical examples are given for the Gauss-Seidel algorithm.
Moreover, we show that using a formula for theA-norm of the error from Dahlquist, Golub and Nash [1978] very good bounds of the error can be computed almost for free during
the iterations of the conjugate gradient method leading to a reliable stopping criterion.
The work of the first author was partially supported by NSF Grant CCR-950539. 相似文献
14.
Matteo Cepale 《Journal of Difference Equations and Applications》2017,23(10):1707-1736
A Liouville–Green (or WKB) asymptotic approximation theory is developed for a class of almost-diagonal (‘asymptotically diagonal’) linear second-order matrix difference equations. Rigorous and explicitly computable bounds for the error terms are obtained, the asymptotics being made with respect to both, the index and some parameter affecting the equation. The case of the associated inhomogeneous equations is also considered in detail. Some examples and a number of applications are presented for the purpose of illustration. 相似文献
15.
Some bounds are given for the deviation and interpolation points of a functionf based on bounds forf
(n+2)/f
(n+1). These bounds are in terms of the deviation and interpolation points ofe
vx
, –1 x 1, wherev is a parameter. The behavior of these points asv is also discussed.The results of this paper are contained in the second author's Master's thesis submitted to the University of Wyoming in May 1969. 相似文献
16.
Some new error bounds for linear complementarity problems of H-matrices are presented based on the preconditioned technique. Numerical examples show that these bounds are better than some existing ones. 相似文献
17.
By introducing redundant Klee–Minty examples, we have previously shown that the central path can be bent along the edges of
the Klee–Minty cubes, thus having 2
n
−2 sharp turns in dimension n. In those constructions the redundant hyperplanes were placed parallel with the facets active at the optimal solution. In
this paper we present a simpler and more powerful construction, where the redundant constraints are parallel with the coordinate-planes.
An important consequence of this new construction is that one of the sets of redundant hyperplanes is touching the feasible
region, and N, the total number of the redundant hyperplanes is reduced by a factor of n
2, further tightening the gap between iteration-complexity upper and lower bounds. 相似文献
18.
We prove explicit upper and lower bounds for the L
1-moment spectra for the Brownian motion exit time from extrinsic metric balls of submanifolds P
m
in ambient Riemannian spaces N
n
. We assume that P and N both have controlled radial curvatures (mean curvature and sectional curvature, respectively) as viewed from a pole in N. The bounds for the exit moment spectra are given in terms of the corresponding spectra for geodesic metric balls in suitably
warped product model spaces. The bounds are sharp in the sense that equalities are obtained in characteristic cases. As a
corollary we also obtain new intrinsic comparison results for the exit time spectra for metric balls in the ambient manifolds
N
n
themselves. 相似文献
19.
Jae Ryong Kweon 《Numerical Methods for Partial Differential Equations》2004,20(3):412-431
A linearized compressible viscous Stokes system is considered. The a posteriori error estimates are defined and compared with the true error. They are shown to be globally upper and locally lower bounds for the true error of the finite element solution. Some numerical examples are given, showing an efficiency of the estimator. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 412–431, 2004. 相似文献
20.
Michael Krivelevich 《Random Structures and Algorithms》1995,7(2):145-155
We develop a new approach for proving lower bounds for various Ramsey numbers, based on using large deviation inequalities. This approach enables us to obtain the bounds for the off-diagonal Ramsey numbers R(Kr, Kk), r ≤ k, that match the best known bounds, obtained through the local lemma. We discuss also the bounds for a related Ramsey-type problem and show, for example, that there exists a K4-free graph G on n vertices in which every cn3/5 log1/2 n vertices span a copy of K3. © 1995 John Wiley & Sons, Inc. 相似文献