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11.
This paper is concerned with the implementation and testing of an algorithm for solving constrained least-squares problems. The algorithm is an adaptation to the least-squares case of sequential quadratic programming (SQP) trust-region methods for solving general constrained optimization problems. At each iteration, our local quadratic subproblem includes the use of the Gauss–Newton approximation but also encompasses a structured secant approximation along with tests of when to use this approximation. This method has been tested on a selection of standard problems. The results indicate that, for least-squares problems, the approach taken here is a viable alternative to standard general optimization methods such as the Byrd–Omojokun trust-region method and the Powell damped BFGS line search method. 相似文献
12.
陈泽乾 《数学物理学报(B辑英文版)》2002,22(3)
A new framework of Gaussian white noise calculus is established, in line with generalized expansion in [3, 4, 7]. A suitable frame of Fock expansion is presented on Gaussian generalized expansion functionals being introduced here, which provides the integral kernel operator decomposition of the second quantization of Koopman operators for chaotic dynamical systems, in terms of annihilation operators dt and its dual, creation operators t*. 相似文献
13.
基于局部多项式逼近的变参数梯度估计算法 总被引:1,自引:0,他引:1
本文分析了梯度辨识算法跟踪时变系统的缺点,提出了一种新的基于局部多项式逼近的变参数梯度估计算法。本算法具有良好跟踪性能特别适用于时变系统跟踪且其对噪声的敏感程度与一般梯度估计方法相当。仿真结果验证了其良好性能。 相似文献
14.
非傍轴平顶高斯光束M2因子两种定义的比较研究 总被引:3,自引:2,他引:1
基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式·研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关·使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较·在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关·按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1,2,3时,M2因子分别趋于0.913,0.882和0.886·当N→∞时,M2因子取最小值M2min=0.816· 相似文献
15.
非傍轴平顶高斯光束M2因子两种定义的比较研究 总被引:1,自引:1,他引:0
基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式.研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关.使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较.在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关.按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1, 2, 3时,M2因子分别趋于0.913,0.882和0.886.当N→∞时,M2因子取最小值M2min=0.816. 相似文献
16.
Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that
have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more.
The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section
2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is
completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated
by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather
suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties
of completely irreducible operators are different from properties of unicellular operators.
__________
Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29 相似文献
17.
Propagation of the Hermite–Gaussian beams through misaligned optical system with a circular aperture
By means of expanding a hard-edged aperture into a finite sum of complex Gaussian functions, the approximate analytical formula of one kind of higher-order Gaussian beams called the Hermite–Gaussian beams (HGBs) passing through circular apertured and misaligned optical system is obtained in this paper. The result provides more convenience for studying its propagation than the usual way by using diffraction integral directly. Some numerical simulations are also given for illustrating the propagation properties of the HGBs through the circular apertured optical systems. 相似文献
18.
The propagation property of flattened Gaussian beams (FGBs) is studied based on the Collins formula, and analytical propagation equations for FGBs with and without an aperture are derived. It is shown that the closed-form expressions for the FGB of order N passing through paraxial ABCD optical systems without an aperture can be written as the combinations of Confluent Hyper-geometric Functions, and that the analytical equations for the FGB of order N passing through apertured paraxial ABCD optical systems may involve Error Functions. The proposed algorithms for the considered beams can save computing time, provide intuitive physical insights, and help to design optical systems. Our results are confirmed and illustrated with numerical examples. 相似文献
19.
20.
We investigate the dynamics of the Λ system driven by two resonant laser fields in presence of dissipation for coupling strengths where the rotating‐wave approximation starts to break down. This regime is characterised by Rabi frequencies being approximately equal or smaller than the field frequencies. A systematic procedure to obtain an expansion for the solution of the Bloch evolution equations of the system is presented. The lowest contribution results to be the well‐known rotating‐wave approximation. The method is based on a semi‐classical treatment of the problem, and its predictions are interpreted fully quantum mechanically. The theory is illustrated by a detailed study of the disappearance of coherent population trapping as the intensities of the fields increase. 相似文献