共查询到20条相似文献,搜索用时 31 毫秒
1.
Fridrich Sloboda 《Numerische Mathematik》1980,35(2):223-230
Summary A generalized conjugate gradient algorithm which is invariant to a nonlinear scaling of a strictly convex quadratic function is described, which terminates after at mostn steps when applied to scaled quadratic functionsf: R
n
R1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andhC
1 (R1) an arbitrary strictly monotone functionh. The algorithm does not suppose the knowledge ofh orF but only off(x) and its gradientg(x). 相似文献
2.
For a bounded regular Jordan domain in R
2, we introduce and study a new class of functions K() related on its Green function G. We exploit the properties of this class to prove the existence and the uniqueness of a positive solution for the singular nonlinear elliptic equation u+(x,u)=0, in D(), with u=0 on and uC(), where is a nonnegative Borel measurable function in ×(0,) that belongs to a convex cone which contains, in particular, all functions (x,t)=q(x)t
–,>0 with nonnegative functions qK(). Some estimates on the solution are also given. 相似文献
3.
F. A. Sukochev 《Integral Equations and Operator Theory》1996,26(1):102-124
If is a surjective isometry of the separable symmetric operator spaceE(M, ) associated with the approximately finite-dimensional semifinite factorM and if ·
E(M,)
is not proportional to ·
L
2, then there exist a unitary operatorUM and a Jordan automorphismJ ofM such that(x)=UJ(x) for allxME(M, ). We characterize also surjective isometries of vector-valued symmetric spacesF((0, 1), E(M, )).Research supported by the Australian Research Council 相似文献
4.
Li Fuan 《数学学报(英文版)》1989,5(2):146-158
LetA andR be commutative rings, andm andn be integers3. It is proved that, if :St
m (A)St
n (R) is an isomorphism, thenm=n. Whenn4, we have: (1) Every isomorphism :St
n(A)St
n(R) induces an isomorphism:E
n (A)E
n (R), and is uniquely determined by; (2) IfSt
n (A) St
n (R) thenK
2.n
(A)K
2.n
(R); (3) Every isomorphismE
n (A) E
n (R) can be lifted to an isomorphismSt
n(A)St
n(R); (4)St
n(A) St
n(R) if and only ifAR. For the casen=3, ifSt
3(A) andSt
3(R) are respectively central extensions ofE
3(A) andE
3 (R), then the above (1) and (2) hold.The Project supported by National Natural Science Foundation of China 相似文献
5.
Stephan Ruscheweyh 《Numerische Mathematik》1984,45(2):227-240
Summary Given a complex polynomialp we determine a functionf
p
: such that |p(f
p
(z))||p(z)|,z withk<1. This result is used to introduce a global root-finding algorithm for polynomials. 相似文献
6.
Wilhelm Forst 《Numerische Mathematik》1978,30(2):137-147
Summary Letx
0<x
1<...<x
n–1<x
0+2 be nodes having multiplicitiesv
0,...,v
n–1, 1v
k
r (0k<n). We approximate the evaluation functional
,x fixed, and the integral respectively by linear functionals of the form
and determine optimal weights
for the Favard classesW
r
C
2. In the even case
of optimal interpolation these weights are unique except forr=1,x(x
k
+x
k–1)/2 mod 2. Moreover we get periodic polynomial splinesw
k, j
(0k<n, 0j<v
k
) of orderr such that
are the optimal weights. Certain optimal quadrature formulas are shown to be of interpolatory type with respect to these splines. For the odd case
of optimal interpolation we merely have obtained a partial solution.
Bojanov hat in [4, 5] ähnliche Resultate wie wir erzielt. Um Wiederholungen zu vermeiden, werden Resultate, deren Beweise man bereits in [4, 5] findet, nur zitiert 相似文献
7.
H. Scheerer 《manuscripta mathematica》1985,51(1-3):63-87
Let R be a subring of the rationals with 1/2, 1/3R; let S
R
n
denote the R-local n-sphere and define
R
n
:=S
R
n
for n odd,
R
n
:=S
R
n
for n>0 even. An H-space (resp. a 1-conn. co-H-space) is decomposable over R, if it is homotopy equivalent to a weak product of spaces
R
n
(resp. to a wedge of R-local spheres). We prove that, if E is grouplike decomposable of finite type over R, the functor [-,E] is determined on finite dim. complexes by the Hopf algebra M*(E;R); here M* denotes the unstable cohomotopy functor of H.J. Baues. If C is cogrouplike decomposable over R, the functor [C,-] is determined on 1-conn. R-local spaces by *(C) as a cogroup in the category of M-Lie algebras. For R = the functor [-,E] is also determined by the Lie algebra *(E) and [C,-] by the Berstein coalgebra associated to the comultiplication of C. 相似文献
8.
D. Y. Ye 《Journal of Optimization Theory and Applications》1993,76(2):287-304
LetA(·) be ann × n symmetric affine matrix-valued function of a parameteruR
m
, and let (u) be the greatest eigenvalue ofA(u). Recently, there has been interest in calculating (u), the subdifferential of atu, which is useful for both the construction of efficient algorithms for the minimization of (u) and the sensitivity analysis of (u), namely, the perturbation theory of (u). In this paper, more generally, we investigate the Legendre-Fenchel conjugate function of (·) and the -subdifferential (u) of atu. Then, we discuss relations between the set (u) and some perturbation bounds for (u).The author is deeply indebted to Professor J. B. Hiriart-Urruty who suggested this study and provided helpful advice and constant encouragement. The author also thanks the referees and the editors for their substantial help in the improvement of this paper. 相似文献
9.
Wilhelm Niethammer 《Numerische Mathematik》1980,34(3):271-283
Summary A nonlinear generalizationÊ
z
of Euler's series transformation is compared with the (linear) Euler-Knopp transformationE
z
and a twoparametric methodE
. It is shown how to applyE
orE
, to compute the valuef(zo) of a functionf from the power series at 0 iff is holomorphic in a half plane or in the cut plane. BothE
andE
, are superior toÊ
z
. A compact recursive algorithm is given for computingE
andE
,. 相似文献
10.
On the entropic regularization method for solving min-max problems with applications 总被引:4,自引:0,他引:4
Consider a min-max problem in the form of min
xX
max1im
{f
i
(x)}. It is well-known that the non-differentiability of the max functionF(x) max1im
{f
i
(x)} presents difficulty in finding an optimal solution. An entropic regularization procedure provides a smooth approximationF
p(x) that uniformly converges toF(x) overX with a difference bounded by ln(m)/p, forp > 0. In this way, withp being sufficiently large, minimizing the smooth functionF
p(x) overX provides a very accurate solution to the min-max problem. The same procedure can be applied to solve systems of inequalities, linear programming problems, and constrained min-max problems.This research work was supported in part by the 1995 NCSC-Cray Research Grant and the National Textile Center Research Grant S95-2. 相似文献
11.
Pavel Valtr 《Discrete and Computational Geometry》1992,7(1):135-152
For a finite setA of points in the plane, letq(A) denote the ratio of the maximum distance of any pair of points ofA to the minimum distance of any pair of points ofA. Fork>0 letc
(k) denote the largest integerc such that any setA ofk points in general position in the plane, satisfying
for fixed
, contains at leastc convex independent points. We determine the exact asymptotic behavior ofc
(k), proving that there are two positive constants=(), such thatk
1/3c
(k)k
1/3. To establish the upper bound ofc
(k) we construct a set, which also solves (affirmatively) the problem of Alonet al. [1] about the existence of a setA ofk points in general position without a 7-hole (i.e., vertices of a convex 7-gon containing no other points fromA), satisfying
. The construction uses Horton sets, which generalize sets without 7-holes constructed by Horton and which have some interesting properties. 相似文献
12.
Prof. Dr. Hansjoachim Groh 《Geometriae Dedicata》1981,11(1):69-98
The notion pasting sum
(P
i
,
i
) of two R
2-planes (or Salzmann planes) (P
i
,
i
) is developed. Necessary and sufficient conditions for it to be an R
2-plane again are given. The notion is applied to classify all flat projective planes whose collineation group contains a sub-group with (isomorphism type of , fixed element configuration)=(2, x). 相似文献
13.
The Bass–Heller–Swan–Farrell–Hsiang–Siebenmann decomposition of the Whitehead group K
1(A[z,z-1]) of a twisted Laurent polynomial extension A[z,z-1] of a ring A is generalized to a decomposition of the Whitehead group K
1(A((z))) of a twisted Novikov ring of power series A((z))=A[[z]][z-1]. The decomposition involves a summand W1(A, ) which is an Abelian quotient of the multiplicative group W(A,) of Witt vectors 1+a1z+a2z2+ ··· A[[z]]. An example is constructed to show that in general the natural surjection W(A, )ab W1(A, ) is not an isomorphism. 相似文献
14.
In-Suk Wee 《Probability Theory and Related Fields》1990,85(4):469-488
Summary Let {X
t
} be a 1 process with stationary independent increments and its Lévy measurev be given byv{yy>x}=x
–L
1
(x), v{yy<–x}=x
–L
2
(x) whereL
1,L
2 are slowly varying at 0 and and 0<1. We construct two types of a nondecreasing functionh(t) depending on 0<<1 or =1 such that lim inf
a.s. ast 0 andt for some positive finite constantC.This research is partialy supported by a grant from Korea University 相似文献
15.
We give uniform estimates of entire functions of exponential type less than having sufficiently small logarithmic sums over real sequences {
n
} satisfying |
n
–n|L and
n+1–
n
for fixed positive constants L and . We thereby generalize results about logarithmic sums over the set of integers and so-called relatively h-dense sequences. 相似文献
16.
Martin Krüskemper 《manuscripta mathematica》1989,65(2):225-243
In this paper we examine for which Witt classes ,..., n over a number field or a function fieldF there exist a finite extensionL/F and 2,..., n L* such thatT
L/F
()=1 andTr
L/F
(i)=i fori=2,...n. 相似文献
17.
A. S. Zinov'ev 《Mathematical Notes》1972,12(5):743-746
We obtain sufficient conditions for the absolute convergence of Fourier series for functions of L
d
2
depending on the properties of the function being expanded and the rate of growth of the sums
of the system of functions {k(t)} orthonormalized in [a, b] with respect to d(t). We show that if at some point x [a, b] the function (t) has a discontinuity, at that point the Fourier series of any functionf(t) L
d
2
, converges absolutely.Translated from Matematicheskie Zametki, Vol. 12, No. 5, pp. 511–516, November, 1972. 相似文献
18.
Stefan Veldsman 《Monatshefte für Mathematik》1996,122(3):227-238
The relationship between the radical of a ringR and a structural matrix ring overR has been determined for some radicals. We continue these investigations, amongst others, determining exactly which radicals have the property (M(,R))=M(
s
,(R))+M(
a
,+(R))for any structural matrix ringM(,R) and finding (M(,R)) for any hereditary subidempotent radical . 相似文献
19.
Xiao-Qing Jin 《BIT Numerical Mathematics》1996,36(1):101-109
We study methods for solving the constrained and weighted least squares problem min
x
by the preconditioned conjugate gradient (PCG) method. HereW = diag (1, ,
m
) with 1
m
0, andA
T
= [T
1
T
, ,T
k
T
] with Toeplitz blocksT
l
R
n × n
,l = 1, ,k. It is well-known that this problem can be solved by solving anaugmented linear 2 × 2 block linear systemM +Ax =b, A
T
= 0, whereM =W
–1. We will use the PCG method with circulant-like preconditioner for solving the system. We show that the spectrum of the preconditioned matrix is clustered around one. When the PCG method is applied to solve the system, we can expect a fast convergence rate.Research supported by HKRGC grants no. CUHK 178/93E and CUHK 316/94E. 相似文献
20.
N. L. Gordeev 《Journal of Mathematical Sciences》2003,116(1):2961-2971
Let be a linear representation of a finite group over a field of characteristic 0. Further, let R
be the corresponding algebra of invariants, and let P
(t) be its Hilbert–Poincaré series. Then the series P
(t) represents a rational function (t)/(t). If R
is a complete intersection, then (t) is a product of cyclotomic polynomials. Here we prove the inverse statement for the case where is an almost regular (in particular, regular) representation of a cyclic group. This yields an answer to a question of R. Stanley in this very special case. Bibliography: 3 titles. 相似文献