where gjΩ for 1jn−1 and arrival times for x1,x2,…,xn, we describe a cubic-time algorithm that determines a circuit for f over Ω that is of linear size and whose delay is at most 1.44 times the optimum delay plus some small constant.  相似文献   

10.
On accuracy of approximation of the spectral radius by the Gelfand formula     
Victor Kozyakin   《Linear algebra and its applications》2009,431(11):2134-2141
The famous Gelfand formula ρ(A)=limsupnAn1/n for the spectral radius of a matrix is of great importance in various mathematical constructions. Unfortunately, the range of applicability of this formula is substantially restricted by a lack of estimates for the rate of convergence of the quantities An1/n to ρ(A). In the paper this deficiency is made up to some extent. By using the Bochi inequalities we establish explicit computable estimates for the rate of convergence of the quantities An1/n to ρ(A). The obtained estimates are then extended for evaluation of the joint spectral radius of matrix sets.  相似文献   

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1.
For n1, let {xjn}nj=1 be n distinct points in a compact set K and letLn[·] denote the corresponding Lagrange interpolation operator. Let v be a suitably restricted function on K. What conditions on the array {xjn}1jnn1 ensure the existence of p>0 such that limn→∞ (fLn[f]) vLp(K)=0 for very continuous fK→ ? We show that it is necessary and sufficient that there exists r>0 with supn1 πnvLr(K) ∑nj=1 (1/|πn| (xjn))<∞. Here for n1, πn is a polynomial of degree n having {xjn}nj=1 as zeros. The necessity of this condition is due to Ying Guang Shi.  相似文献   

2.
3.
If u ≥ 0 is subharmonic on a domain Ω in n and 0 < p < 1, then it is well-known that there is a constant C(n,p) ≥ 1 such u(x)pC)n,p) MV )up,B(x,r)) for each ball B(x,r)) Ω. We show more generally that a similar result holds for functions ψ : ++ may be any surjective, concave function whose inverse ψ−1 satisfies the Δ2-condition.  相似文献   

4.
Galerkin methods are used to approximate the singular integral equation
with solution φ having weak singularity at the endpoint −1, where a, b≠0 are constants. In this case φ is decomposed as φ(x)=(1−x)α(1+x)βu(x), where β=−α, 0<α<1. Jacobi polynomials are used in the discussions. Under the conditions fHμ[−1,1] and k(t,x)Hμ,μ[−1,1]×[−1,1], 0<μ<1, the error estimate under a weighted L2 norm is O(nμ). Under the strengthened conditions fHμ[−1,1] and , 2α<μ<1, the error estimate under maximum norm is proved to be O(n2αμ+), where , >0 is a small enough constant.  相似文献   

5.
Let 1<p<∞, and k,m be positive integers such that 0(k−2m)pn. Suppose ΩRn is an open set, and Δ is the Laplacian operator. We will show that there is a sequence of positive constants cj such that for every f in the Sobolev space Wk,p(Ω), for all xΩ except on a set whose Bessel capacity Bk−2m,p is zero.  相似文献   

6.
Let E be a real reflexive Banach space with uniformly Gâteaux differentiable norm. Let K be a nonempty bounded closed and convex subset of E. Let T:KK be a strictly pseudo-contractive map and let L>0 denote its Lipschitz constant. Assume F(T){xK:Tx=x}≠0/ and let zF(T). Fix δ(0,1) and let δ* be such that δ*δL(0,1). Define , where δn(0,1) and limδn=0. Let {αn} be a real sequence in (0,1) which satisfies the following conditions: . For arbitrary x0,uK, define a sequence {xn}K by xn+1=αnu+(1−αn)Snxn. Then, {xn} converges strongly to a fixed point of T.  相似文献   

7.
For the weight function (1−x2)μ−1/2 on the unit ball, a closed formula of the reproducing kernel is modified to include the case −1/2<μ<0. The new formula is used to study the orthogonal projection of the weighted L2 space onto the space of polynomials of degree at most n, and it is proved that the uniform norm of the projection operator has the growth rate of n(d−1)/2 for μ<0, which is the smallest possible growth rate among all projections, while the rate for μ0 is nμ+(d−1)/2.  相似文献   

8.
Let m and n be positive integers with n2 and 1mn−1. We study rearrangement-invariant quasinorms R and D on functions f: (0, 1)→ such that to each bounded domain Ω in n, with Lebesgue measure |Ω|, there corresponds C=C(|Ω|)>0 for which one has the Sobolev imbedding inequality R(u*(|Ωt))CD(|mu|* (|Ωt)), uCm0(Ω), involving the nonincreasing rearrangements of u and a certain mth order gradient of u. When m=1 we deal, in fact, with a closely related imbedding inequality of Talenti, in which D need not be rearrangement-invariant, R(u*(|Ωt))CD((d/dt) ∫{x n : |u(x)|>u*(|Ωt)} |(u)(x)| dx), uC10(Ω). In both cases we are especially interested in when the quasinorms are optimal, in the sense that R cannot be replaced by an essentially larger quasinorm and D cannot be replaced by an essentially smaller one. Our results yield best possible refinements of such (limiting) Sobolev inequalities as those of Trudinger, Strichartz, Hansson, Brézis, and Wainger.  相似文献   

9.
We consider boolean circuits C over the basis Ω={,} with inputs x1, x2,…,xn for which arrival times are given. For 1in we define the delay of xi in C as the sum of ti and the number of gates on a longest directed path in C starting at xi. The delay of C is defined as the maximum delay of an input.Given a function of the form
f(x1,x2,…,xn)=gn−1(gn−2(…g3(g2(g1(x1,x2),x3),x4)…,xn−1),xn)
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