作者：
WONG, YSNASA
LANGLEY RES CTRINST COMP APPL SCI & ENGNHAMPTONVA 23665 MCGILL UNIV
MONTREAL H3A 2T5QUEBECCANADA
A new computational technique for the solution of the full potential equation is presented. The method consists of outer and inner iterations. The outer iteration is based on a Newton-like algorithm;a preconditioned m...
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A method for designing robust feedback controllers for multiloop systems is presented. Robustness is characterized in terms of the minimum singular value of the system return difference matrix at the plant input. Anal...
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Reference is made to a recent paper by B. J. Cardwell and C. J. Goodman (published in IEE Proc. B, Electr. Power Appl. , 1984, 131, (3), pp. 91-98) who calculate the optimal controls for a dc machine executing transie...
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Reference is made to a recent paper by B. J. Cardwell and C. J. Goodman (published in IEE Proc. B, Electr. Power Appl. , 1984, 131, (3), pp. 91-98) who calculate the optimal controls for a dc machine executing transient changes in speed. Their computational method is capable of dealing with armature current saturation but, unfortunately, encounters convergence difficulties in the presence of control limits. In this correspondence, the conjugate gradient algorithm is shown to overcome this difficulty. A reply by the original authors is included.
The information-based study of the optimal solution of large linear systems is initiated by studying the case of Krylov information. Among the algorithms that use Krylov information are minimal residual, conjugate gra...
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The information-based study of the optimal solution of large linear systems is initiated by studying the case of Krylov information. Among the algorithms that use Krylov information are minimal residual, conjugategradient, Chebyshev, and successive approximation algorithms. A "sharp" lower bound on the number of matrix-vector multiplications required to compute an å-approximation is obtained for any orthogonally invariant class of matrices. Examples of such classes include many of practical interest such as symmetric matrices, symmetric positive definite matrices, and matrices with bounded condition number. It is shown that the minimal residual algorithm is within at most one matrix-vector multiplication of the lower bound. A similar result is obtained for the generalized minimal residual algorithm. The lower bound is computed for certain classes of orthogonally invariant matrices. How the lack of certam properties (symmetry, positive definiteness) increases the lower bound is shown. A conjecture and a number of open problems are stated.
We have studied previously a generalized conjugategradient method for solving sparse positive-definite systems of linear equations arising from the discretization of elliptic partial-differential boundary-value probl...
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We have studied previously a generalized conjugategradient method for solving sparse positive-definite systems of linear equations arising from the discretization of elliptic partial-differential boundary-value problems. Here, extensions to the nonlinear case are considered. We split the original discretized operator into the sum of two operators, one of which corresponds to a more easily solvable system of equations, and accelerate the associated iteration based on this splitting by (nonlinear) conjugategradients. The behavior of the method is illustrated for the minimal surface equation with splittings corresponding to nonlinear SSOR, to approximate factorization of the Jacobian matrix, and to elliptic operators suitable for use with fast direct methods. The results of numerical experiments are given as well for a mildy nonlinear example, for which, in the corresponding linear case, the finite termination property of the conjugate gradient algorithm is crucial.
The equivalence of problems in structural analysis to certain variational statements has traditionally been used as a means of formulating field equations and natural boundary conditions. In recent years developments ...
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