TY - JOUR TI - On the relation between the behavior and the distribution of the zeros of a polynomial AU - Huang, K AU - Li, Zhilin T2 - Journal of Nanjing University, Mathematics Biquarterly DA - 1985/// PY - 1985/// VL - 2 IS - 1 SP - 53–59 ER - TY - CONF TI - On the numerical approximations for linear functional differential equations with input and output delays AU - Tran, Hien AU - Manitius, A. T2 - 1985 24th IEEE Conference on Decision and Control AB - In this paper we state some new results on the approximations for linear retarded functional differential equations with delays in control and observation. We consider the finite difference (i.e., averaging) approximation scheme for such systems treated as evolution equations in the state space setup, and we establish several basic properties of the approximation scheme. These results are extensions of recent results of Lasiecka and ManitiusL1 to the case of systems with input and output delays. C2 - 1985/12// C3 - 1985 24th IEEE Conference on Decision and Control CY - Fort Lauderdale, FL DA - 1985/12// PY - 1985/12/11/ DO - 10.1109/cdc.1985.268746 PB - IEEE UR - http://dx.doi.org/10.1109/cdc.1985.268746 ER - TY - JOUR TI - Computation of closed-loop eigenvalues associated with the optimal regulator problem for functional differential equations AU - Manitius, A. AU - Tran, H. T2 - IEEE Transactions on Automatic Control AB - A solution of the linear quadratic control problem involving functional differential equations gives a linear feeback which modifies the original system dynamics. Under certain assumptions, the eigenvalues of the modified system constitute a stable part of the spectrum of a certain Hamiltonian operator. These eigenvalues can be computed without solving the infinite-dimensional Riccati equation. In this note we present a method to compute the eigenvalues directly from a characteristic equation of the optimal closed-loop system. Numerical results are presented for three examples and compared to those obtained by a finite-dimensional approximation of a functional differential equation. DA - 1985/12// PY - 1985/12// DO - 10.1109/tac.1985.1103866 VL - 30 IS - 12 SP - 1245-1248 J2 - IEEE Trans. Automat. Contr. LA - en OP - SN - 0018-9286 UR - http://dx.doi.org/10.1109/tac.1985.1103866 DB - Crossref ER - TY - JOUR TI - Broyden's method for approximate solution of nonlinear integral equations AU - Kelley, C.T. AU - Sachs, E.W. T2 - Journal of Integral Equations DA - 1985/// PY - 1985/// VL - 9 IS - 1 SP - 25–44 ER - TY - JOUR TI - Why does the {F_N}-Method work? AU - Kelley, C T AU - Mullikin, T W T2 - Trans. Th. Stat. Phys. DA - 1985/// PY - 1985/// VL - 14 SP - 513-526 ER - TY - CONF TI - Analytical determination of normal contact stresses for arbitrary geometries with application to the tire/pavement interaction mechanism AU - Clapp, T G AU - Kelley, C T AU - Eberhardt, A C T2 - American Society for Testing and Materials A2 - Gillespie, T D A2 - Sayers, M C2 - 1985/// C3 - Measuring Road Roughness and its Effects on User Cost and Comfort CY - Baltimore DA - 1985/// SP - 162-178 ER - TY - JOUR TI - Expanded Convergence Domains for Newton’s Method at Nearly Singular Roots AU - Decker, D. W. AU - Kelley, C. T. T2 - SIAM Journal on Scientific and Statistical Computing AB - We consider Newton’s method for a class of nonlinear equations for which the derivative is nearly singular at the root. We show that there is a larger than expected domain of attraction for the Newton iterates but that convergence appears to be only linear in most of this domain. We give a modification of Newton’s method that improves this slow convergence. DA - 1985/10// PY - 1985/10// DO - 10.1137/0906064 VL - 6 IS - 4 SP - 951-966 J2 - SIAM J. Sci. and Stat. Comput. LA - en OP - SN - 0196-5204 2168-3417 UR - http://dx.doi.org/10.1137/0906064 DB - Crossref ER - TY - JOUR TI - Broyden’s Method for a Class of Problems Having Singular Jacobian at the Root AU - Decker, D. W. AU - Kelley, C. T. T2 - SIAM Journal on Numerical Analysis AB - For a class of nonlinear equations $F(x) = 0$, in $\mathbb{R}^n $, with the Jacobian $F'$ being singular at a root, $x^ * $, Broyden’s method is shown to yield a sequence that converges linearly to $x^ * $ if the initial guess is chosen in a special region. The asymptotic linear rate is ${{(\sqrt 5 - 1)} / 2}$. DA - 1985/6// PY - 1985/6// DO - 10.1137/0722034 VL - 22 IS - 3 SP - 566-574 J2 - SIAM J. Numer. Anal. LA - en OP - SN - 0036-1429 1095-7170 UR - http://dx.doi.org/10.1137/0722034 DB - Crossref ER - TY - JOUR TI - Why does the -method work? AU - Kelley, C.T. AU - Mullikin, T.W. T2 - Transport Theory and Statistical Physics DA - 1985/// PY - 1985/// VL - 14 SP - 513–526 ER -