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81.
Renato Spigler Marco Vianello 《Proceedings of the American Mathematical Society》1996,124(6):1763-1771
Rigorous asymptotic approximations of the WKB (or Liouville-Green) type are obtained for a basis of solutions to in the framework of -algebras. Both cases and are included, thus generalizing the classical theory for scalar equations developed by F.W.J. Olver to matrix as well as to infinite-dimensional equations.
82.
Z. Ditzian 《Proceedings of the American Mathematical Society》1996,124(6):1773-1781
We show that the -functional
where , is equivalent to the rate of convergence of a certain linear polynomial operator. This operator stems from a Riesz-type summability process of expansion by Legendre polynomials. We use the operator above to obtain a linear polynomial approximation operator with a rate comparable to that of the best polynomial approximation.
83.
A good preconditioner is extremely important in order for the conjugate gradients method to converge quickly. In the case of Toeplitz matrices, a number of recent studies were made to relate approximation of functions to good preconditioners. In this paper, we present a new result relating the quality of the Toeplitz preconditionerC for the Toeplitz matrixT to the Chebyshev norm (f– g)/f, wheref and g are the generating functions forT andC, respectively. In particular, the construction of band-Toeplitz preconditioners becomes a linear minimax approximation problem. The case whenf has zeros (but is nonnegative) is especially interesting and the corresponding approximation problem becomes constrained. We show how the Remez algorithm can be modified to handle the constraints. Numerical experiments confirming the theoretical results are presented. 相似文献
84.
L. Brutman 《Numerical Algorithms》1993,5(9):437-442
Generalized alternating polynomials have been introduced by the author earlier. In the present paper their indirect analogue is constructed for numerical solution of the Fredholm linear integral equations. Although the proposed method is a particular case of the general projection scheme, its valuable feature is the presence of a sequence of parameters, which, for sufficiently smooth kernels and inhomogeneous terms, serves as an indicator of the quality of approximation. 相似文献
85.
The probability of first return to the initial intervalx and the diffusion tensorD
x are calculated exactly for a ballistic Lorentz gas on a Bethe lattice or Cayley tree. It consists of a moving particle and a fixed array of scatterers, located at the nodes, and the lengths of the intervals between scatterers are determined by a geometric distribution. The same values forx andD
x apply also to a regular space lattice with a fraction of sites occupied by a scatterer in the limit of a small concentration of scatterers. If backscattering occurs, the results are very different from the Boltzmann approximation. The theory is applied to different types of lattices and different types of scatterers having rotational or mirror symmetries. 相似文献
86.
We have upgraded a Self-consistent-field – Hartree–Fock routine to include a finite nuclear mass correction for molecules developed in our laboratory. The new routine can handle isotopomers without calculating any nuclear kinetic energy matrix element. Tests on H2, LiH, HF, F2, and H2O isotopomers indicate the equivalence of our correction to the standard diagonal adiabatic correction. A further original application to C2H6 illustrates the usefulness of the method for polyatomic molecules. The resulting molecular orbitals carry the nuclear mass signature, exemplified with Koopmans ionization potentials.From the Proceedings of the 28th Congreso de Químicos Teóricos de Expresión Latina (QUITEL 2002) 相似文献
87.
We are dealing with a numerical method for solving the problem of minimizing a difference of two convex functions (a d.c. function) over a closed convex set in
n
. This algorithm combines a new prismatic branch and bound technique with polyhedral outer approximation in such a way that only linear programming problems have to be solved.Parts of this research were accomplished while the third author was visiting the University of Trier, Germany, as a fellow of the Alexander von Humboldt foundation. 相似文献
88.
In this paper we study constraint qualifications and duality results for infinite convex programs (P) = inf{f(x): g(x) – S, x C}, whereg = (g
1,g
2) andS = S
1 ×S
2,S
i
are convex cones,i = 1, 2,C is a convex subset of a vector spaceX, andf andg
i
are, respectively, convex andS
i
-convex,i = 1, 2. In particular, we consider the special case whenS
2 is in afinite dimensional space,g
2 is affine andS
2 is polyhedral. We show that a recently introduced simple constraint qualification, and the so-called quasi relative interior constraint qualification both extend to (P), from the special case thatg = g
2 is affine andS = S
2 is polyhedral in a finite dimensional space (the so-called partially finite program). This provides generalized Slater type conditions for (P) which are much weaker than the standard Slater condition. We exhibit the relationship between these two constraint qualifications and show how to replace the affine assumption ong
2 and the finite dimensionality assumption onS
2, by a local compactness assumption. We then introduce the notion of strong quasi relative interior to get parallel results for more general infinite dimensional programs without the local compactness assumption. Our basic tool reduces to guaranteeing the closure of the sum of two closed convex cones. 相似文献
89.
Chu-In Charles Lee 《Annals of the Institute of Statistical Mathematics》1992,44(1):107-120
The Laplace continued fraction is derived through a power series. It provides both upper bounds and lower bounds of the normal tail probability % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x), it is simple, it converges for x>0, and it is by far the best approximation for x3. The Laplace continued fraction is rederived as an extreme case of admissible bounds of the Mills' ratio, % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiqbfA6agzaaraaaaa!3DC0!\[\bar \Phi\](x)/(x), in the family of ratios of two polynomials subject to a monotone decreasing absolute error. However, it is not optimal at any finite x. Convergence at the origin and local optimality of a subclass of admissible bounds are investigated. A modified continued fraction is proposed. It is the sharpest tail bound of the Mills' ratio, it has a satisfactory convergence rate for x1 and it is recommended for the entire range of x if a maximum absolute error of 10-4 is required.The efforts of the author were supported by the NSERC of Canada. 相似文献
90.
Protein kinases are an important class of enzymes controlling virtually all cellular signaling pathways. Consequently, selective inhibitors of protein kinases have attracted significant interest as potential new drugs for many diseases. Computational methods, including molecular docking, have increasingly been used in the inhibitor design process [1]. We have considered several docking packages in order to strengthen our kinase inhibitor work with computational capabilities. In our experience, AutoDock offered a reasonable combination of accuracy and speed, as opposed to methods that specialize either in fast database searches or detailed and computationally intensive calculations.However, AutoDock did not perform well in cases where extensive hydrophobic contacts were involved, such as docking of SB203580 to its target protein kinase p38. Another shortcoming was a hydrogen bonding energy function, which underestimated the attraction component and, thus, did not allow for sufficiently accurate modeling of the key hydrogen bonds in the kinase-inhibitor complexes.We have modified the parameter set used to model hydrogen bonds, which increased the accuracy of AutoDock and appeared to be generally applicable to many kinase-inhibitor pairs without customization. Binding to largely hydrophobic sites, such as the active site of p38, was significantly improved by introducing a correction factor selectively affecting only carbon and hydrogen energy grids, thus, providing an effective, although approximate, treatment of solvation. 相似文献