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1.
Let f C[a, b]. LetP be a subset ofC[a, b], L b – a be a given real number. We say thatp P is a best approximation tof fromP, with arc length constraintL, ifA[p] b a [1 + (p(x)) 2]dx L andp – f q – f for allq P withA[q] L. represents an arbitrary norm onC[a, b]. The constraintA[p] L might be interpreted physically as a materials constraint.In this paper we consider the questions of existence, uniqueness and characterization of constrained best approximations. In addition a bound, independent of degree, is found for the arc length of a best unconstrained Chebyshev polynomial approximation.The work of L. L. Keener is supported by the National Research Council of Canada Grant A8755.  相似文献   

2.
Zhang  Yin  Zhang  Detong 《Mathematical Programming》1994,66(1-3):361-377
At present the interior-point methods of choice are primal—dual infeasible-interior-point methods, where the iterates are kept positive, but allowed to be infeasible. In practice, these methods have demonstrated superior computational performance. From a theoretical point of view, however, they have not been as thoroughly studied as their counterparts — feasible-interior-point methods, where the iterates are required to be strictly feasible. Recently, Kojima et al., Zhang, Mizuno and Potra studied the global convergence of algorithms in the primal—dual infeasible-interior-point framework. In this paper, we continue to study this framework, and in particular we study the local convergence properties of algorithms in this framework. We construct parameter selections that lead toQ-superlinear convergence for a merit function andR-superlinear convergence for the iteration sequence, both at rate 1 + where can be arbitrarily close to one.Research supported in part by NSF DMS-9102761 and DOE DE-FG05-91ER25100.Corresponding author.  相似文献   

3.
Weyl's theorem for operator matrices   总被引:11,自引:0,他引:11  
Weyl's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues of finite multiplicity. By comparison Browder's theorem holds for an operator when the complement in the spectrum of the Weyl spectrum coincides with Riesz points. Weyl's theorem and Browder's theorem are liable to fail for 2×2 operator matrices. In this paper we explore how Weyl's theorem and Browder's theorem survive for 2×2 operator matrices on the Hilbert space.Supported in part by BSRI-97-1420 and KOSEF 94-0701-02-01-3.  相似文献   

4.
Letw=(w 1,,w m ) andv=(v 1,,v m-1 ) be nonincreasing real vectors withw 1>w m andv 1>v m-1 . With respect to a lista 1,,a n of linear orders on a setA ofm3 elements, thew-score ofaA is the sum overi from 1 tom ofw i times the number of orders in the list that ranka inith place; thev-score ofaA{b} is defined in a similar manner after a designated elementb is removed from everya j .We are concerned with pairs (w, v) which maximize the probability that anaA with the greatestw-score also has the greatestv-score inA{b} whenb is randomly selected fromA{a}. Our model assumes that linear ordersa j onA are independently selected according to the uniform distribution over them linear orders onA. It considers the limit probabilityP m (w, v) forn that the element inA with the greatestw-score also has the greatestv-score inA{b}.It is shown thatP m (m,v) takes on its maximum value if and only if bothw andv are linear, so thatw i w i+1=w i+1w i+2 forim–2, andv i –v i+1 =v i+1 –v i+2 forim–3. This general result for allm3 supplements related results for linear score vectors obtained previously form{3,4}.  相似文献   

5.
In this paper the steady-state behavior of many symmetric queues, under the head of the line processor-sharing discipline, is investigated. The arrival process to each of n queues is Poisson, with rateA, and each queue hasr waiting spaces. A job arriving at a full queue is lost. The queues are served by a single exponential server, which has a mean raten, and splits its capacity equally amongst the jobs at the head of each nonempty queue. The normal traffic casep=/< 1 is considered, and it is assumed thatn1 andr= 0(1). A 2-term asymptotic approximation to the loss probabilityL is derived, and it is found thatL = 0(n r ), for fixedp. If6=(1–p)/p 1, then the approximation is valid if n2 1 and (r+ 1)2n, and in this caseL r!/(n)r. Numerical values ofL are obtained forr = 1,2,3,4 and 5,n = 1000,500 and 200, and various values ofp< 1. Very small loss probabilities may be obtained with appropriate values of these parameters.  相似文献   

6.
It is known by H. Sachs [5] that the classical curve theorem of ABRAMESCU also holds in isotropic geometry. Generalising an idea due to O. Röschel [2] we regard all inscribed parabolas (s, t) of a triangle (t). This triangle is formed by the tangents of three neighbouring points of a C -curve k(t) in an isotropic plane. Let U((t)) be the circumcircle of (t) and I((t)) the incircle of the triangle (t) whose midpoints of the sides are the vertices of (t). The circle U((t)) is the locus of the isotropic focal points of (s, t) and the incircle I((T)) the envelope of the isotropic axes of (s, t). We prove that the ABRAMESU-circle — lim U((t)) — is identical with the locus of the focal points of lim (s, t) and the circle lim I((t)) with the envelope of the axes of lim (s, t). The characteristic points, different from k(t), of the circles lim U((t)) and lim I((t)) determine the direction of the affine-normal of k(t).Herrn Professor Helmut Mäurer zum 60. Geburtstag gewidmet  相似文献   

7.
By the M.Riesz Convexity Theorem, an operator T on the space of simple integrable functions into the measurable functions (on some measure space) which has continuous extensions to Lp() and Lq() , where 1 p q , also has continuous exten — sions to all Lr () , p r q . It is shown that, whenever (Tp) and (Tq) are o-dimensional (in particular, countable) then the spectra (Tr) (p r q) are pairwise identical. For q = , only w*-continuous extensions are considered. An example due to Dayanithy shows that the conclusion fails in general.  相似文献   

8.
Q (.. , L). Q . P(Sr(2)) — 2 (S r(2) (r — ). , M(P(S r(m=sup{t(·)t(·)1:t P(S r(2)),t 0}. , /4+(1)M(P(S r(2)))/r 215/17+(1)(r+). (Q), Q L.  相似文献   

9.
We consider the approximation of the function (x) and its derivative '(x) on [a, b] given that (x)C 2,N, i.e., belongs to the class of functions f(x) that satisfy the conditions f(x)L, f(xi)=yi, i=1,,N, where L and yi are given real numbers and xi are the nodes of an arbitrary grid, a=x1<x2<<XN=b. A solution algorithm on the class of functions C2,L,N is proposed which has optimal accuracy with a constant not exceeding 2. A bound on the approximation error of the function and its derivative is derived.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 56, pp. 57–61, 1985  相似文献   

10.
On affine scaling algorithms for nonconvex quadratic programming   总被引:8,自引:0,他引:8  
We investigate the use of interior algorithms, especially the affine-scaling algorithm, to solve nonconvex — indefinite or negative definite — quadratic programming (QP) problems. Although the nonconvex QP with a polytope constraint is a hard problem, we show that the problem with an ellipsoidal constraint is easy. When the hard QP is solved by successively solving the easy QP, the sequence of points monotonically converge to a feasible point satisfying both the first and the second order optimality conditions.Research supported in part by NSF Grant DDM-8922636 and the College Summer Grant, College of Business Administration, The University of Iowa.  相似文献   

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