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181.
Previous results on quasi-classical limit of the KP hierarchy and itsW-infinity symmetries are extended to the Toda hierarchy. The Planck constant now emerges as the spacing unit of difference operators in the Lax formalism. Basic notions, such as dressing operators, Baker-Akhiezer functions, and tau function, are redefined.W
1 + symmetries of the Toda hierarchy are realized by suitable rescaling of the Date-Jimbo-Kashiara-Miwa vertex operators. These symmetries are contracted tow
1 + symmetries of the dispersionless hierarchy through their action on the tau function. 相似文献
182.
Robert D. Skeel 《BIT Numerical Mathematics》1993,33(1):172-175
For fixed step-sizeh the Störmer method is stable for the standard test equationÿ=
2
y,>0, if and only ifh<2. We show that for variable step sizeh
n there does not exist a (positive) limit onh which ensures stability. Nor can we guarantee stability if, in addition, we limit the step size ratioh
n/h
n–1.This work was supported in part by National Science Foundation Grant DMS 90 15533. 相似文献
183.
Inge Söderkvist 《BIT Numerical Mathematics》1993,33(4):687-694
Given two arbitrary real matricesA andB of the same size, the orthogonal Procrustes problem is to find an orthogonal matrixM such that the Frobenius norm MA – B is minimized. This paper treats the common case when the orthogonal matrixM is required to have a positive determinant. The stability of the problem is studied and supremum results for the perturbation bounds are derived. 相似文献
184.
Giuseppe Savaré 《Numerische Mathematik》1993,65(1):319-335
Summary We study the approximation of linear parabolic Cauchy problems by means of Galerkin methods in space andA -stable multistep schemes of arbitrary order in time. The error is evaluated in the norm ofL
t
2
(H
x
1
) L
t
(L
x
2
). 相似文献
185.
The stability and convergence of the solutions of perturbed and regularized variational inequality to the solutions of the primary (unstable a priori) variational inequality with proper monotone operator are investigated. All the objects of inequality: the operatorA, the right-hand partf and the set of constrains are to be perturbed. At the same time no assumptions of boundedness and smoothness of the operatorA are used. The connection between the parameters of perturbations, which guarantees strong convergence of approximate solutions, is established. It is proved that the existence of the solution to the unperturbed variational inequality is necessary and sufficient condition for convergence of the regularized perturbed inequality solutions.This research was supported in part by the Ministry of Science Grant 3481-1-91 and by the Ministry of Absorption Center for Absorption in Science. 相似文献
186.
A spectral Galerkin approximation of the Orr-Sommerfeld eigenvalue problem in a semi-infinite domain
Thomas M. Fischer 《Numerische Mathematik》1993,66(1):159-179
Summary The convergence of a Galerkin approximation of the Orr-Sommerfeld eigenvalue problem, which is defined in a semi-infinite domain, is studied theoretically. In case the system of trial functions is based on a composite of Jacobi polynomials and an exponential transform of the semi-infinite domain, the error of the Galerkin approximation is estimated in terms of the transformation parametera and the numberN of trial functions. Finite or infinite-order convergence of the spectral Galerkin method is obtained depending on how the transformation parameter is chosen. If the transformation parameter is fixed, then convergence is of finite order only. However, ifa is varied proportional to 1/N
with an exponent 0<<1, then the approximate eigenvalue converges faster than any finite power of 1/N asN. Some numerical examles are given. 相似文献
187.
Summary We present here a new hybrid method for the iterative solution of large sparse nonsymmetric systems of linear equations, say of the formAx=b, whereA
N, N
, withA nonsingular, andb
N
are given. This hybrid method begins with a limited number of steps of the Arnoldi method to obtain some information on the location of the spectrum ofA, and then switches to a Richardson iterative method based on Faber polynomials. For a polygonal domain, the Faber polynomials can be constructed recursively from the parameters in the Schwarz-Christoffel mapping function. In four specific numerical examples of non-normal matrices, we show that this hybrid algorithm converges quite well and is approximately as fast or faster than the hybrid GMRES or restarted versions of the GMRES algorithm. It is, however, sensitive (as other hybrid methods also are) to the amount of information on the spectrum ofA acquired during the first (Arnoldi) phase of this procedure. 相似文献
188.
Knut Petras 《Numerische Mathematik》1993,65(1):121-133
Summary For functions with an interior singularity, the errors of a class of positive quadrature formulae with high algebraic degree are reduced to those of the much simpler Euler-Maclaurin type formulae. Applying this method to certain classes of functions, such as, for example,f(x)=h(x)|x-u|
, where >–1, with a sufficiently smooth functionh, we obtain the main term of the error expansion for quadrature rules of ultraspherical type. 相似文献
189.
Summary In a simply connected planar domainD the expected lifetime of conditioned Brownian motion may be viewed as a function on the set of hyperbolic geodesics for the domain. We show that each hyperbolic geodesic induces a decomposition ofD into disjoint subregions
and that the subregions are obtained in a natural way using Euclidean geometric quantities relating toD. The lifetime associated with on each
j
is then shown to be bounded by the product of the diameter of the smallest ball containing
j
and the diameter of the largest ball in
j
. Because this quantity is never larger than, and in general is much smaller than, the area of the largest ball in
j
it leads to finite lifetime estimates in a variety of domains of infinite area.Research of the first author was supported in part by NSF Grant DMS-9100811Research of the second author was supported in part by NSF Grant DMS-9105407 相似文献
190.
Summary In earlier works, the gauge theorem was proved for additive functionals of Brownian motion of the form
0
t
q(B
s
)ds, whereq is a function in the Kato class. Subsequently, the theorem was extended to additive functionals with Revuz measures in the Kato class. We prove that the gauge theorem holds for a large class of additive functionals of zero energy which are, in general, of unbounded variation. These additive functionals may not be semi-martingales, but correspond to a collection of distributions that belong to the Kato class in a suitable sense. Our gauge theorem generalizes the earlier versions of the gauge theorem.Research supported in part by NSA grant MDA-92-H-30324 相似文献