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The problems of computing least squares approximations for various types of real and symmetric matrices subject to spectral constraints share a common structure. This paper describes a general procedure in using the projected gradient method. It is shown that the projected gradient of the objective function on the manifold of constraints usually can be… (More)

- Moody T. Chu, Robert Funderlic, Gene H. Golub
- SIAM Review
- 1995

Let A 2 R mn denote an arbitrary matrix. If x 2 R n and y 2 R m are vectors such that ! = y T Ax 6 = 0, then the matrix B := A ? ! ?1 Axy T A has rank exactly one less than the rank of A. This Wedderburn rank-one reduction formula is easy to prove, yet the idea is so powerful that perhaps all matrix factorizations can be derived from it. The formula also… (More)

- Moody T. Chu
- 2007

Any logical procedure that is used to reason or infer either deductively or inductively so as to draw conclusions or make decisions can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state gets developed into another state by following a certain specific rule. Such an action is qualified… (More)

This paper concerns the construction of a structured low rank matrix that is nearest to a given matrix. The notion of structured low rank approximation arises in various applications, ranging from signal enhancement to protein folding to computer algebra, where the empirical data collected in a matrix do not maintain either the specified structure or the… (More)

- Moody T. Chu
- SIAM Review
- 1998

A collection of inverse eigenvalue problems are identiied and classiied according to their characteristics. Current developments in both the theoretic and the algorithmic aspects are summarized and reviewed in this paper. This exposition also reveals many open questions that deserves further study. An extensive bibliography of pertinent literature is… (More)

- Moody T. Chu
- 2002

An inverse eigenvalue problem concerns the reconstruction of a structured matrix from prescribed spectral data. Such an inverse problem arises in many applications where parameters of a certain physical system are to be determined from the knowledge or expectation of its dynamical behavior. Spectral information is entailed because the dynamical behavior… (More)

- SPIS TREŚCI, Bernardo Cockburn, +44 authors Michael Eisermann
- 2010

1 Superconvergent discontinuous Galerkin methods for second-order elliptic problems / A multiscale finite element method for partial differential equations posed in domains with rough boundaries / Alexandre L. Madureira 35 Convergence and optimality of adaptive mixed finite element methods / 79 Overlapping additive Schwarz preconditioners for elliptic PDEs… (More)

- Moody T. Chu, J. Loren Watterson
- SIAM J. Scientific Computing
- 1993

- Moody T. Chu, Yuen-Cheng Kuo, Wen-Wei Lin
- SIAM J. Matrix Analysis Applications
- 2004

The inverse eigenvalue problem of constructing real and symmetric square matrices M, C and K of size n × n for the quadratic pencil Q(λ) = λ 2 M + λC + K so that Q(λ) has a prescribed subset of eigenvalues and eigenvectors is considered. This paper consists of two parts addressing two related but different problems. The first part deals with the inverse… (More)

- Moody T. Chu, Shu-Fang Xu
- Math. Comput.
- 2009

Spectral decomposition provides a canonical representation of an operator over a vector space in terms of its eigenvalues and eigenfunctions. The canonical form often facilitates discussions which, otherwise, would be complicated and involved. Spectral decomposition is of fundamental importance in many applications. The well-known GLR theory generalizes the… (More)