Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gradient methods, i...
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Two Armijo-type line searches are proposed in this paper for nonlinear conjugate gradient methods. Under these line searches, global convergence results are established for several famous conjugate gradient methods, including the Fletcher-Reeves method, the Polak-Ribiere-Polyak method, and the conjugate descent method.
A generalized AKNS isospectral problem where the trace of corresponding spectral matrix is not zero, is transformed to a new isospectral problem where the trace of the resulting matrix is zero, by using transformation...
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A generalized AKNS isospectral problem where the trace of corresponding spectral matrix is not zero, is transformed to a new isospectral problem where the trace of the resulting matrix is zero, by using transformation of Lax pairs, and these two spectral problems lead to the same hierarchy of equations. The authors started from the transformed spectral problem and constructed a new loop algebra which has not appeared before, and obtained the integrable coupling of the generalized AKNS hierarchy. Specially, the integrable couplings of the KdV equation and MKdV equation are obtained.
We propose a new scheme for modeling a smooth interpolatory surface, from a surface discretization consisting of triangles, quadrilaterals and pentagons, by algebraic surface patches which are subsets of real zero con...
In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences, by a trust region-CG algorithm. Image restoration involves the removal or minimization...
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In this paper we solve large scale ill-posed problems, particularly the image restoration problem in atmospheric imaging sciences, by a trust region-CG algorithm. Image restoration involves the removal or minimization of degradation (blur, clutter, noise, etc.) in an image using a priori knowledge about the degradation phenomena. Our basic technique is the so-called trust region method, while the subproblem is solved by the truncated conjugate gradient method, which has been well developed for well-posed *** trust region method, due to its robustness in global convergence, seems to be a promising way to deal with ill-posed problems.
We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with...
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We study the symmetric positive semidefinite solution of the matrix equation AX_1A^T + BX_2B^T=C. where A is a given real m×n matrix. B is a given real m×p matrix, and C is a given real m×m matrix, with m, n, p positive integers: and the bisymmetric positive semidefinite solution of the matrix equation D^T XD=C, where D is a given real n×m matrix. C is a given real m×m matrix, with m. n positive integers. By making use of the generalized singular value decomposition, we derive general analytic formulae, and present necessary and sufficient conditions for guaranteeing the existence of these solutions.
The multi-symplectic formulations of the Good Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman inte...
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The multi-symplectic formulations of the Good Boussinesq equation were considered. For the multi-symplectic formulation, a new fifteen-point difference scheme which is equivalent to the multi-symplectic Preissman integrator was derived. The numerical experiments show that the multi-symplectic schemes have excellent long-time numerical behavior.
＜正＞In this paper,we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg-Marquardt type method to solve the nonlinear ...
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＜正＞In this paper,we convert the nonlinear complementarity problems to an equivalent smooth nonlinear equation system by using smoothing technique. Then we use Levenberg-Marquardt type method to solve the nonlinear equation *** global and local superlinear convergence properties of the method are obtained under very mild ***,the algorithm is locally super-linearly convergent without assumption of strict complementarity of the solutions and uniqueness of the solution of NCP.
Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference...
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Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for HamiltonJacobiequations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.
Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Dis...
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Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Discussion of the discrete form of the D-N alternating algorithm.
Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N...
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Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; Numerical results of the study.
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