共查询到20条相似文献,搜索用时 15 毫秒
1.
We study the worst case tractability of multivariate linear problems defined on separable Hilbert spaces. Information about a problem instance consists of noisy evaluations of arbitrary bounded linear functionals, where the noise is either deterministic or random. The cost of a single evaluation depends on its precision and is controlled by a cost function. We establish mutual interactions between tractability of a problem with noisy information, the cost function, and tractability of the same problem, but with exact information. 相似文献
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In this paper we revisit the classical problem of polynomial interpolation, with a slight twist; namely, polynomial evaluations are available up to a group action of the unit circle on the complex plane. It turns out that this new setting allows for a phaseless recovery of a polynomial in a polynomial time. 相似文献
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A generalized Newton method for absolute value equations 总被引:4,自引:1,他引:4
O. L. Mangasarian 《Optimization Letters》2009,3(1):101-108
A direct generalized Newton method is proposed for solving the NP-hard absolute value equation (AVE) Ax − |x| = b when the singular values of A exceed 1. A simple MATLAB implementation of the method solved 100 randomly generated 1,000-dimensional AVEs to an accuracy
of 10−6 in less than 10 s each. Similarly, AVEs corresponding to 100 randomly generated linear complementarity problems with 1,000 ×
1,000 nonsymmetric positive definite matrices were also solved to the same accuracy in less than 29 s each. 相似文献
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In this paper we present an efficient numerical algorithm for solving linear and nonlinear boundary value problems with two-point
boundary conditions of tenth-order. The differential transform method is applied to construct the numerical solutions. The
proposed algorithm avoids the complexity provided by other numerical approaches. Several illustrative examples are given to
demonstrate the effectiveness of the present algorithm.
相似文献
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Absolute value programming 总被引:4,自引:0,他引:4
O. L. Mangasarian 《Computational Optimization and Applications》2007,36(1):43-53
We investigate equations, inequalities and mathematical programs involving absolute values of variables such as the equation
Ax+B|x| = b, where A and B are arbitrary m× n real matrices. We show that this absolute value equation is NP-hard to solve, and that solving it with B = I solves the general linear complementarity problem. We give sufficient optimality conditions and duality results for absolute
value programs as well as theorems of the alternative for absolute value inequalities. We also propose concave minimization
formulations for absolute value equations that are solved by a finite succession of linear programs. These algorithms terminate
at a local minimum that solves the absolute value equation in almost all solvable random problems tried. 相似文献
8.
Absolute value equation solution via concave minimization 总被引:3,自引:0,他引:3
O. L. Mangasarian 《Optimization Letters》2007,1(1):3-8
The NP-hard absolute value equation (AVE) Ax − |x| = b where and
is solved by a succession of linear programs. The linear programs arise from a reformulation of the AVE as the minimization of a piecewise-linear concave function on a polyhedral set and solving the latter by successive linearization. A simple MATLAB implementation of the successive linearization algorithm solved 100 consecutively generated 1,000-dimensional random instances of the AVE with only five violated equations out of a total of 100,000 equations. 相似文献
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We present a semi-analytical iterative method for solving nonlinear second order multi-point boundary value problems. To demonstrate the working of the method we consider a particular example of this class of problems. In this example, we demonstrate the accuracy and convergence of the method to the solution. We demonstrate clearly that the method is accurate, fast and has a reasonable order of convergence. 相似文献
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Rehana Bari 《Journal of Mathematical Analysis and Applications》2004,292(1):17-22
For any integer m?2, we consider the 2mth order boundary value problem
(−1)mu(2m)(x)=λg(u(x))u(x),x∈(−1,1), 相似文献
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The existence of solutions to a class of two-point boundary value problems in three-ion electrodiffusion is investigated via an integro-differential formulation. Boundedness by upper and lower solutions corresponding to associated boundary value problems is considered and illustrated by Painlevé II solutions of a constrained version of the original boundary value problems. 相似文献
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In this research, we study linear difference equations with constant coefficients subject to boundary conditions. Necessary and/or sufficient conditions for the existence of a unique solution will be established. The proofs of the existence and uniqueness theorems are established by means of special types of determinants called Mosaic Vandermonde determinants. 相似文献
15.
In this paper, a novel method is proposed for solving nonlinear two-point boundary value problems (BVPs). This method is based on a combination of the Adomian decomposition method (ADM) and the reproducing kernel method (RKM). A major advantage of this method over standard ADM is that it can avoid unnecessary computation in determining the unknown parameters. The proposed method can be applied to singular and nonsingular BVPs. Numerical results obtained using the scheme presented here show that the numerical scheme is very effective and convenient for solving nonlinear two-point boundary value problems. 相似文献
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Wu-jun Sun 《高校应用数学学报(英文版)》2010,25(1):9-17
In this paper nonlinear boundary value problems for discontinuous delayed differen- tial equations are considered. Some existence and boundedness results of solutions are obtained via the method of upper and lower solutions, which may be discontinuous. Our analysis can be applied to those phenomena from physics and control theory which have been successfully described by delayed differential equations with discontinuous functions, such as electric, pneu- matic, and hydraulic networks. It is also an important step to precede the design of control signals when finite-time or practical stability control are concerned. 相似文献
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In this letter we give a less restrictive condition compared to that given by Zhang and Chen (2010), for first order initial conditions to be recoverable with a particular classical or nonclassical symmetry generator. Examples are provided for the generalised Kuramoto–Sivashinsky equation and a nonlinear diffusion equation with a sink term. 相似文献