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31.
Seymour V. Parter 《Applied mathematics and computation》1985,17(2):137-151
Several recent papers have discussed the convergence of the multigrid V-cycle. In particular there are several results for the symmetric case: where the numbers of smoothings before the fine-to-coarse transfer and after the coarse-to-fine transfer are the same. In most instances, the smoother H=I?E-1A has been limited to the case where E is positive definite and the eigenvalues h of H satisfy 0?h?1. In this note we extend these results to asymmetric V-cycles and the case where -b?h?1 with 0<b<1. 相似文献
32.
This paper describes techniques that can be used to transform PDEs with variable coefficients into equations with constant coefficients. The techniques are illustrated by calculating shear flows over quite general surfaces, by solving the signaling problem for diffusive processes in inhomogeneous materials, and by solving the signaling problem for acoustical waves when the sound speed varies with distance. The techniques may also be used to solve equations governing processes in inhomogeneous, anisotropic materials. 相似文献
33.
34.
Seymour Meyerson 《Journal of mass spectrometry : JMS》1989,24(4):267-270
The appearance a decade ago of the concept of ion-neutral complexes as intermediates in unimolecular decompositions constituted a major advance in mechanistic interpretation of mass spectra. The concept, however, was not new; it goes back to the introduction of the cationated cyclopropane in the mid-1950s. Its development did not occur via a smooth progression; rather, its history bridges a sharp discontinuity. The early workers, in a curious historical quirk, failed to generalize on the idea beyond complexes in which the neutral component is cyclopropane or a closely related species. Hence it took an independent rediscovery of the concept to usher in the rapid growth and wide application that characterize its present stage of development. 相似文献
35.
36.
37.
Seymour V. Parter 《Numerische Mathematik》1988,52(6):701-723
Summary TheMGR[v] algorithms of Ries, Trottenberg and Winter, the Algorithms 2.1 and 6.1 of Braess and the Algorithm 4.1 of Verfürth are all multigrid algorithms for the solution of the discrete Poisson equation (with Dirichlet boundary conditions) based on red-black Gauss-Seidel smoothing. Both Braess and Verfürth give explicit numerical upper bounds on the rate of convergence of their methods in convex polygonal domains. In this work we reconsider these problems and obtain improved estimates for theh–2h Algorithm 4.1 as well asW-cycle estimates for both schemes in non-convex polygonal domains. The proofs do not depend on the strengthened Cauchy inequality.Sponsored by the Air Force Office of Scientific Research under Contract No. AFOSR-86-0163 相似文献
38.
P.D Seymour 《Journal of Combinatorial Theory, Series B》1981,30(2):130-135
We prove that every graph with no isthmus has a nowhere-zero 6-flow, that is, a circulation in which the value of the flow through each edge is one of ±1, ±2,…, ±5. This improves Jaeger's 8-flow theorem, and approaches Tutte's 5-flow conjecture. 相似文献
39.
A single orthogonalized plane wave calculation has been made, to zero order in the pseudopotential, of the direct contact Knight shift for 30 liquid metals. The average deviation from experimental values is approximately 15%. Larger unexplained divergences occur for Cu and Hg. In addition it is shown that to zero order in the pseudopotential the factorΩP F in the Knight shift describing the electron density at the nucleus is almost unaffected by thermal expansion. 相似文献
40.
P. D. Seymour 《Combinatorica》1982,2(1):91-97
De Bruijn and Erdős proved that ifA
1, ...,A
k
are distinct subsets of a set of cardinalityn, and |A
i
∩A
j
|≦1 for 1≦i<j ≦k, andk>n, then some two ofA
1, ...,A
k
have empty intersection. We prove a strengthening, that at leastk /n ofA
1, ...,A
k
are pairwise disjoint. This is motivated by a well-known conjecture of Erdőds, Faber and Lovász of which it is a corollary.
Partially supported by N. S. F. grant No. MCS—8103440 相似文献