M. K. H. Fan# #A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix## Linear Algebra and Its Applications#vol. 188# 189# pp. 231#253# 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....programming problem is an extension of linear programming (LP) Specifically if the condition that X is a diagonal matrix is added to the constraint set then (1.1) reduces to linear programming. Semidefinite programs arise in a wide variety of applications from control theory (see [VB93] and [Fan93]) to combinatorial optimization (see section 5 below) and even structural computational complexity theory (see [FL92] The oldest form of semidefinite programming is the evaluation of eigenvalues of a symmetric matrix. In fact, one can reformulate the classical theorems of Rayleigh Ritz for the ....

M. Fan. A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix. Linear Algebra and its Applications, 188,189:207--230, 1993.

....results for eigenvalues and eigenprojections of [21, 24] as well as the pioneering work of [14] M. L. Overton introduced in [36] a local metric which enables him to obtain a quadratically converging algorithm for (P ) This approach was then developed further in [37] 39] 38] 44] and [13]. Roughly speaking, assume that the multiplicity r of 1 (A(x ) at an optimal point x is known; then the approach consists in minimizing the maximum eigenvalue subject to the constraint that its multiplicity is r. A local C 2 parametrization of (P ) is then used to develop a ....

M. K. H Fan. A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix. Linear Algebra Appl., 188-189:231-253, 1993.

....Another aspect of concern is the computational complexity of the algorithm. We found that, typical of linear convergence, the error was significantly reduced in a small number of iterations, and the rest of the time was spent reducing the error by small amounts. Further research with local methods [22, 23, 24] may improve the convergence rate close to a local minimum. 6. A Design Example Given an ideal filter response, we show some of the considerations in implementing an PBTV system. The example introduces new concepts such as transition regions for a PBTV system. Also, the example shows the behavior ....

M. K. H. Fan, "A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix," Linear Algebra and Its Applications, vol. 188, 189, pp. 231--253, 1993.

....programming problem is an extension of linear programming (LP) Specifically if the condition that X is a diagonal matrix is added to the constraint set then (1.1) reduces to linear programming. Semidefinite programs arise in a wide variety of applications from control theory (see [63] and [20]) to combinatorial optimization (see section 5 below) and even structural computational complexity theory (see [21] The oldest form of semidefinite programming is the evaluation of eigenvalues of a symmetric matrix. In fact, one can reformulate the classical theorems of Rayleigh Ritz for the ....

M. Fan, A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix, Linear Algebra Appl., 188,189 (1993), pp. 207--230.

....observed in practice; this feature is mentioned in [28] and was also observed for all designs done using this algorithm. Third, local convergence of the method might be accelerated using optimization methods tailored to the structure of the problem. Many advances have been made towards this goal [30, 31, 32]. 6. An Example We consider the model matching problem shown in Figure 10. The output of a ratechanging system with a real coefficient, length 51 FIR filter, H, is compared to a ratechanging system with an ideal filter, H ideal . For this problem, L = 2 and M = 5, so H and 20 Figure 10. ....

M. K. H. Fan, "A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix," Linear Algebra and Its Applications, vol. 188, 189, pp. 231--253, 1993.

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M. K. H. Fan# #A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix## Linear Algebra and Its Applications#vol. 188# 189# pp. 231#253# 1993.

No context found.

M. K. H. Fan# #A quadratically convergent local algorithm on minimizing the largest eigenvalue of a symmetric matrix## Linear Algebra and Its Applications#vol. 188# 189# pp. 231#253# 1993.

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