S. Friedland, J. Nocedal and M. L. Overton (1987), `The formulation and analysis of numerical methods for inverse eigenvalue problems', SIAM J. Numer. Anal. 24, 634-667. Home/Search Document Not in Database Summary Related Articles Check |
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An Inexact Cayley Transform Method For Inverse Eigenvalue.. - Zheng-Jian Bai Raymond (2003) (Correct)
....as follows: Given n real numbers 1 Delta Delta Delta n , find c 2 R such that i (c) i for i = 1; n. Our goal in this paper is to derive an efficient algorithm for solving the IEP especially when n is large. Two examples were mentioned in Friedland, Nocedal, and Overton [4] where one needs to solve IEP with large n: the inverse Sturm Liouville problem where n is the number of grid points and in nuclear spectroscopy where n is the number of measurements. We note that the IEP can be formulated as a system of nonlinear equations f (c) j ( 1 (c) Gamma 1 ; ....
....and CUHK DAG 2060220. morini ciro.de.unifi.it) Dipartimento di Energetica S. Stecco Universit a di Firenze, Via C. Lombroso 6 17, 50134 Firenze. Research was partially supported by MIUR, Rome, Italy, through Cofinanziamenti Programmi di Ricerca Scientifica di Interesse Nazionale . In [4], different Newton like methods for solving (2) are given. One of their methods, Method III, forms the approximate Jacobian equation by applying matrix exponentials and Cayley transforms. In each Newton iteration (the outer iteration) we need to solve the approximate Jacobian equation. When n is ....
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S. Friedland, J. Nocedal, and M. Overton, The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems, SIAM J. Numer. Anal., 24 (1987), 634--667. 11
The Inexact Newton-Like Method for Inverse Eigenvalue Problem - Raymond Chan Chung (2001) (Correct)
....problem (IEP) is defined as follows: For n given real numbers f i=1 where 1 Delta Delta Delta n , find a vector c such that i (c i for i = 1; n. Our goal in this paper is to derive an efficient algorithm for solving the IEP. In Friedland, Nocedal, and Overton [3], the IEP is solved by applying a Newton like method, where in each Newton iteration (the outer iteration) we need to solve two linear systems: i) the inverse power method to find the approximate eigenvectors of the current iterate, and (ii) to solve the approximate Jacobian equation. When n is ....
....methods for solving the IEP. In x3, we introduce our inexact Newton like method. The convergence analysis is given in x4 and we present our numerical results in x5. 2 The Newton Like Method In this section, we briefly recall the Newton and Newton like methods for solving the IEP. For details, see [3]. For any c = c 1 ; c n ) define f : R R by f (c) 1 (c) Gamma 1 ; Delta Delta Delta ; n (c) Gamma ; 2) where i (c) are the eigenvalues of A(c) defined in (1) and i are the given eigenvalues. Clearly, c is a solution to the IEP if and only if f ....
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S. Friedland, J. Nocedal, and M. Overton. The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems, SIAM J. Numer. Anal., 24 (1987), pp. 634-- 667.
Method of Centers for Minimizing Generalized Eigenvalues - Boyd, Ghaoui (1993) (41 citations) (Correct)
....that depends affinely on x. In this case, the problem is in fact convex (but still nondifferentiable) Many researchers have considered this problem. Relevant work includes Cullum et al. [CDW75] Craven and Mond [CM81] Polak and Wardi [PW82] Fletcher [Fle85] Shapiro [Sha85] Friedland et al. [FNO87], Goh and Teo [GT88] Panier [Pan89] Allwright [All89] Overton [Ove88, Ove92, OW93, OW92] Ringertz [Rin91] Fan and Nekooie [FN92] and Fan [Fan92] In [BY89] Boyd and Yang use the cutting plane algorithm and Shor s subgradient method [Sho85] to solve eigenvalue minimization problems that ....
S. Friedland, J. Nocedal, and M. Overton. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal., 24(3):634--667, June 1987. 37
The Theory of a Multi Degree of Freedom Dynamic Absorber - Ram, Elhay (1996) (1 citation) (Correct)
....is as prescribed. Finding such a matrix C (when it exists) for a given D is known as the multiplicative inverse eigenvalue problem [4] and can be solved in closed form for systems of dimension up to three. For higher dimension, finding solutions is more difficult and even state of the art methods [5] are unsatisfactory: among other things, they are iterative and global convergence is not assured. Moreover, general conditions for a solution to exist are not known. A better strategy is to use the approach in [6] see pages 69 75) for constructing the model of a simply connected mass spring ....
S. Friedland, J. Nocedal, and M.L. Overton. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal., 24(3):634--667, 1987.
Interior Point Methods in Semidefinite Programming with.. - Alizadeh (1993) (223 citations) (Correct)
....subgradients of the sum of the first few eigenvalues of a symmetric matrix and formulates optimality conditions for this problem. In the same spirit as Fletcher, Overton [Ove88] studies the largest eigenvalue of a symmetric matrix as a convex, but nondifferentiable function. Based on earlier work [FNO87], in [Ove88] he derives a quadratically convergent algorithm for the problem of minimizing the largest eigenvalue of an affinely constrained matrix. This work is further extended in [Ove92] where both second order methods based on sequential quadratic programming, and first order methods based on ....
S. Friedland, J. Nocedal, and M. L. Overton. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal., 24(3), 1987.
On some Structured Inverse Eigenvalue Problems - Erra, Philippe (1995) (2 citations) (Correct)
....of order n, and A P is the pertransposition of A. A n th order matrix A such that A P = In Delta A T Delta In = A is called a persymmetric matrix. 2 Jacobi Inverse Eigenvalue Problems Discrete Inverse Eigenvalue Problems have first been proposed by Downing and Householder [DH56] see [Fri77, FNO87] for newer references) We limit our attention, in this section, to the following situations which we define as the upper Jacobi Inverse Eigenvalue Problems (an upper Jiep) that has been raised by Hochstadt ( Hoc67] Problem 2.1 Let = f i g i=1 Delta Delta Deltan and Omega = f i g ....
....two families of algorithms that can be used to solve (Jiep) namely the Lanczos algorithm and the Euclid Sturm algorithm with a special emphasis on Routh s algorithm. We point out that we only consider direct or finite algorithms, i.e algorithms that terminate in a finite number of steps. See [FNO87] for a survey of iterative algorithms for inverse eigenvalue problems. 3.1 Euclid Sturm Algorithms The integer Euclid s algorithm is one of the oldest nontrivial algorithms. For a full description see [Knu81] and for a survey see [Bar74] Definition 3.1 Let f and g be two polynomials of ....
S. Friedland, J. Nocedal, and M.L Overton. The formulation and analysis of numerical methods for inverse eigenvalue problems. Siam J. Num. Anal., 24(3):634--667, 1987.
Eigenvalue Optimization - Lewis, al. (1996) (41 citations) Self-citation (Overton) (Correct)
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, 299--316. S. Friedland, J. Nocedal and M. L. Overton (1987), `The formulation and analysis of numerical methods for inverse eigenvalue problems', SIAM J. Numer. Anal.
Optimality Conditions and Duality Theory for Minimizing.. - Overton And Womersley (1993) (35 citations) Self-citation (Overton) (Correct)
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S. Friedland, J. Nocedal and M. L. Overton (1987), "The formulation and analysis of numerical methods for inverse eigenvalue problems", SIAM Journal on Numerical Analysis 24, pp. 634-667.
Large-Scale Optimization of Eigenvalues - Overton (1991) (45 citations) Self-citation (Overton) (Correct)
....minmax optimization techniques (e.g. MO80] cannot be applied. Suggestions 2 for transforming the problem into a standard nonlinear programming form by means of determinants have been made [GT88] but these methods perform poorly [Pan89] for other comments on the use of determinants, see [FNO87] In the example given above, the maximum eigenvalue is convex in x. This is true in general when A depends linearly on x, since the Rayleigh principle can be used to show that the maximum eigenvalue is a convex function of the matrix elements. Because of this fact, it has been recognized for ....
....problems arising in structural engineering. In [Ove88] a quadratically convergent algorithm was given to solve the model problem, using a dual matrix formulation of the optimality conditions to fully exploit the nonsmooth problem structure. Two papers which greatly influenced this work were [FNO87,Fle85] Numerical examples were given, demonstrating quadratic convergence to nonsmooth solutions. The assumption was made that A(x) was affine, although it was indicated that this was not essential for the main ideas to apply. The reason for this is that the eigenvalues are nonsmooth, nonlinear ....
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S. Friedland, J. Nocedal, and M.L. Overton. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM Journal on Numerical Analysis, 24:634--667, 1987.
On The Optimal Design Of Columns Against Buckling - Cox, Overton (1992) (3 citations) Self-citation (Overton) (Correct)
....linearized value for 2 (oe j) does not drop below that for 1 (oe j) and that the various bounds are satisfied. If t = 2, the second through fourth rows of E give a linearization of the appropriate set of three nonlinear equations imposing the coalescence of 1 (oe j) and 2 (oe j) see [16]. The common linearized value, 1 (oe) is maximized, subject to the given constraints. Theorem 6.2. Suppose that = 0 so that the multiplicity estimate t is exact, and suppose that ae 0 and J is the empty set. Then d = 0 is a (nonunique) solution to the linear program given above if and only ....
S. Friedland, J. Nocedal, and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal., 24(1987), pp. 634-- 667.
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S. Friedland, J. Nocedal and M. L. Overton (1987), `The formulation and analysis of numerical methods for inverse eigenvalue problems', SIAM J. Numer. Anal. 24, 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal., 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal., 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), pp. 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal., 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal., 24(1987), 634-667.
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S. Friedland, J. Nocedal and M. L. Overton, The formulation and analysis of numerical methods for inverse eigenvalue problems, SIAM J. Numer. Anal. 24(1987), 634-667.
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S. Friedland, J. Nocedal, and M. L. Overton, "The formulation and analysis of numerical methods for inverse eigenvalue problems," SIAM J. Numer. Anal., pp. 634--667, 1987.
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S. Friedland, J. Nocedal and M. L. Overton, The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems, SIAM J. Numer. Anal., 24 (1987), 634--667.
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S. Friedland, J. Nocedal, and M. Overton, The Formulation and Analysis of Numerical Methods for Inverse Eigenvalue Problems, SIAM J. Numer. Anal., 24 (1987), 634--667.
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S. FRIEDLAND, J. NOCEDAL, and M.L. OVERTON. The formulation and analysis of numerical methods for inverse eigenvalue problems. SIAM J. Numer. Anal., 24(3):634--667, 1987.
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