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91.
F. De Vylder 《Insurance: Mathematics and Economics》1983,2(3):139-145
Let Lj (j = 1, …, n + 1) be real linear functions on the convex set of probability distributions. We consider the problem of maximization of Ln+1(F) under the constraint F ? and the equality constraints L1(F) = z1 (i = 1, …, n). Incorporating some of the equality constraints into the basic set , the problem is equivalent to a problem with less equality constraints. We also show how the dual problems can be eliminated from the statement of the main theorems and we give a new illuminating proof of the existence of particular solutions.The linearity of the functions Lj(j = 1, …, n + 1) can be dropped in several results. 相似文献
92.
93.
We present an ultra compact and high resolution free space optical spectrometer and demonstrate it by using FDTD simulations. The miniature interferometer-based speetrometer is a series of submicron phase objects on a polymethyl methacrylate(PMMA) film with a CCD as the detector. The speetrum is obtained by solving a system of simultaneous linear equations. The Tikhonov regularization method is used to achieve a resolution at the picometer level. Compared with conventional speetrometers, the proposed device is low-cost and easy to fabricate due to its simple structure. Furthermore, its compact feature renders the device ideal for miniaturization and integration as the systems in microfluidics architectures and lab-on-chip designs. 相似文献
94.
Adrian Doicu Olena Schüssler Diego Loyola 《Journal of Quantitative Spectroscopy & Radiative Transfer》2010,111(6):907-916
In this paper we present several constrained regularization methods for ozone profile retrieval from UV/VIS nadir sounding instruments such as GOME, SCIAMACHY, OMI and GOME-2. These methods extend the Tikhonov regularization and the iteratively regularized Gauss-Newton method with equality and inequality constraints imposed on the vertical column. It will be shown that this type of information, which is delivered by an independent algorithm like DOAS or GODFIT, significantly improves the accuracy and stability of the profile retrieval. 相似文献
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97.
In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general H¨older type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock(2005) for choosing the regularization parameter. 相似文献
98.
This work is concerned with identifying a space-dependent source function from noisy final time measured data in a time-fractional diffusion wave equation by a variational regularization approach. We provide a regularity of direct problem as well as the existence and uniqueness of adjoint problem. The uniqueness of the inverse source problem is discussed. Using the Tikhonov regularization method, the inverse source problem is formulated into a variational problem and a conjugate gradient algorithm is proposed to solve it. The efficiency and robust of the proposed method are supported by some numerical experiments. 相似文献
99.
Dozyslav B. Kuryliak Oleksiy M. Sharabura 《Mathematical Methods in the Applied Sciences》2020,43(4):1565-1581
The electromagnetic problem by the finite bicone, which is formed with the perfectly conducting semi-infinite cone and the finite cone with truncated vertex, is studied. Bicone is excited axial-symmetrically by the ring magnetic source. The diffracted field is represented through the series of the transversal magnetic (TM) modes; the lower mode among them is called the transversal electromagnetic wave (TEM). On the basis of this representation and using the mode matching technique, we derive the series equations to determine the unknown complex modes magnitudes. In view of the electric field singularities at the conical edges, these equations are represented in the form of the limiting transition from the finite sums to the series. We derive the rule of this transition, as well as the procedure for reducing them to the infinite system of linear algebraic equations (ISLAE) of the first kind. We study asymptotic properties of the matrix elements and find that the main part of their static limit and their behavior for large indexes form the matrix operator of the convolution type; the corresponding inverted operator in the analytical form is obtained. Both these operators, which we call the regularization operators, are used for the transition from the ISLAE of the first kind to the ISLAE of the second kind. The ISLAE thus obtained allow for the solution of any geometrical parameters and frequency with the given accuracy. The asymptotic properties of their solutions are analyzed, and the numerical examinations of the far field patterns are provided. 相似文献
100.
In this paper, we introduce and analyze a new singular value decomposition (SVD) called weighted SVD (WSVD) using a new inner product instead of the Euclidean one. We use the WSVD to approximate the singular values and the singular functions of the Fredholm integral operators. In this case, the new inner product arises from the numerical integration used to discretize the operator. Then, the truncated WSVD (TWSVD) is used to regularize the Nyström discretization of the first‐kind Fredholm integral equations. Also, we consider the weighted LSQR (WLSQR) to approximate the solution obtained by the TWSVD method for large problems. Numerical experiments on a few problems are used to illustrate that the TWSVD can perform better than the TSVD. 相似文献