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91.
Bosco García-Archilla 《Numerische Mathematik》1992,61(1):291-310
Summary A finite-difference method for the integration of the Korteweg-de Vries equation on irregular grids is analyzed. Under periodic boundary conditions, the method is shown to be supraconvergent in the sense that, though being inconsistent, it is second order convergent. However, such a convergence only takes place on grids with an odd number of points per period. When a grid with an even number of points is used, the inconsistency of the method leads to divergence. Numerical results backing the analysis are presented. 相似文献
92.
Brenton R. Clarke 《Journal of multivariate analysis》2007,98(5):916-931
In this paper, we consider the estimation of a parameter of interest where the estimator is one of the possibly several solutions of a set of nonlinear empirical equations. Since Newton's method is often used in such a setting to obtain a solution, it is important to know whether the so obtained iteration converges to the locally unique consistent root to the aforementioned parameter of interest. Under some conditions, we show that this is eventually the case when starting the iteration from within a ball about the true parameter whose size does not depend on n. Any preliminary almost surely consistent estimate will eventually lie in such a ball and therefore provides a suitable starting point for large enough n. As examples, we will apply our results in the context of M-estimates, kernel density estimates, as well as minimum distance estimates. 相似文献
93.
In this paper we define and study an extension of the g-Drazin for elements of a Banach algebra and for bounded linear operators based on an isolated spectral set rather than on
an isolated spectral point. We investigate salient properties of the new inverse and its continuity, and illustrate its usefulness
with an application to differential equations. Generalized Mbekhta subspaces are introduced and the corresponding extended
Mbekhta decomposition gives a characterization of circularly isolated spectral sets. 相似文献
94.
Jon Wilkening 《Linear algebra and its applications》2007,427(1):6-25
We present an efficient algorithm for obtaining a canonical system of Jordan chains for an n × n regular analytic matrix function A(λ) that is singular at the origin. For any analytic vector function b(λ), we show that each term in the Laurent expansion of A(λ)−1b(λ) may be obtained from the previous terms by solving an (n + d) × (n+d) linear system, where d is the order of the zero of det A(λ) at λ = 0. The matrix representing this linear system contains A(0) as a principal submatrix, which can be useful if A(0) is sparse. The last several iterations can be eliminated if left Jordan chains are computed in addition to right Jordan chains. The performance of the algorithm in floating point and exact (rational) arithmetic is reported for several test cases. The method is shown to be forward stable in floating point arithmetic. 相似文献
95.
LetC(X,E) andC(Y,F) denote the spaces of continuous functions on the Tihonov spacesX andY, taking values in the Banach spacesE andF, respectively. A linear mapH:C(X,E)→C(Y,F) isseparating iff(x)g(x)=0 for allx inX impliesHf(y)Hg(y)=0 for ally inY. Some automatic continuity properties and Banach-Stone type theorems (i.e., asserting that isometries must be of a certain
form) for separating mapsH between spaces of real- and complex-valued functions have already been developed. The extension of such results to spaces
of vector-valued functions is the general subject of this paper. We prove in Theorem 4.1, for example, for compactX andY, that a linear isometryH betweenC(X,E) andC(Y,F) is a “Banach-Stone” map if and only ifH is “biseparating (i.e,H andH
−1 are separating). The Banach-Stone theorems of Jerison and Lau for vector-valued functions are then deduced in Corollaries
4.3 and 4.4 for the cases whenE andF or their topological duals, respectively, are strictly convex.
Research supported by the Fundació Caixa Castelló, MI/25.043/92 相似文献
96.
In this paper we design a fast new algorithm for reducing an N × N quasiseparable matrix to upper Hessenberg form via a sequence of N − 2 unitary transformations. The new reduction is especially useful when it is followed by the QR algorithm to obtain a complete set of eigenvalues of the original matrix. In particular, it is shown that in a number of cases some recently devised fast adaptations of the QR method for quasiseparable matrices can benefit from using the proposed reduction as a preprocessing step, yielding lower cost and a simplification of implementation. 相似文献
97.
Perch Melik-Adamyan 《Complex Analysis and Operator Theory》2007,1(3):423-438
An analog of the Kreĭn–Saakyan formula is derived for any pair of relatively prime self-adjoint extensions of a minimal symmetric
canonical differential operator. This allows us to deduce a trace formula in the matrix case.
I am grateful to Sh. Saakyan for his interest in this work and lively discussion.
Received: December 8, 2006. Accepted: December 30, 2006. 相似文献
98.
Brian Hartwig 《Linear algebra and its applications》2007,422(1):219-235
Recently Terwilliger and the present author found a presentation for the three-point sl2 loop algebra via generators and relations. To obtain this presentation we defined a Lie algebra ? by generators and relations and displayed an isomorphism from ? to the three-point sl2 loop algebra. In this paper we classify the finite-dimensional irreducible ?-modules. 相似文献
99.
Long-period fibre gratings inside standard single-mode optical communication fibres are successfully fabricated with infrared femtosecond laser pulses. The refractive index perturbations are well confined within the fibre core by choosing the proper laser focusing parameters and translation speed of the fibre during the direct laser writing process. With the self-focusing effect considered and at a constant average irradiation dose of 1.62 × 10^3 J/(cm^2μm), the threshold intensity for fabricating long-period gratings with infrared femtosecond laser pulses is determined to be 5.13 × 10^13 W/cm2. 相似文献
100.
An energy-dependent partitioning scheme is explored for extracting a small number of eigenvalues of a real symmetric matrix with the help of genetic algorithm. The proposed method is tested with matrices of different sizes (30 × 30 to 1000 × 1000). Comparison is made with Löwdin’s strategy for solving the problem. The relative advantages and disadvantages of the GA-based method are analyzed 相似文献