Diagonal elements and eigenvalues of a real symmetric matrix

Chan, N. N.; Li, Kim-Hung

doi:10.1016/0022-247x(83)90171-3

Cited by 35 publications

(31 citation statements)

References 4 publications

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“…Therefore, at most (N − 1) rotations are required before the resulting matrix has a unit diagonal. The Chan-Li algorithm, on the other hand, was developed as a constructive proof of the Schur-Horn theorem [4]. Suppose that a λ.…”

Section: 3mentioning

confidence: 99%

“…We now exhibit a different method for transforming the diagonal of A to z while preserving its eigenvalues. It can be viewed as a generalization of the Chan-Li algorithm [4].…”

Section: Generalized Bendel-mickeymentioning

confidence: 99%

“…Refer to [20,22] for details on how the problem arises in wireless applications. Two finite step techniques, the Bendel-Mickey [2] and Chan-Li [4] algorithms, are available for special cases. Both algorithms apply a sequence of plane rotations to an initial matrix that change its diagonal entries while preserving its spectrum.…”

Section: Introductionmentioning

confidence: 99%

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Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum

Dhillon¹,

Heath²,

Sustik³

et al. 2005

SIAM J. Matrix Anal. & Appl.

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Abstract. In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N − 1) or fewer plane rotations, where N is the dimension of the matrix. Both the Bendel-Mickey and the Chan-Li algorithms are special cases of the proposed procedures. Using the fact that a positive semidefinite matrix can always be factored as X * X , we also provide more efficient versions of the algorithms that can directly construct factors with specified singular values and column norms. We conclude with some open problems related to the construction of Hermitian matrices with joint diagonal and spectral properties.

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Section: 3mentioning

confidence: 99%

“…We now exhibit a different method for transforming the diagonal of A to z while preserving its eigenvalues. It can be viewed as a generalization of the Chan-Li algorithm [4].…”

Section: Generalized Bendel-mickeymentioning

confidence: 99%

See 1 more Smart Citation

Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum

Dhillon¹,

Heath²,

Sustik³

et al. 2005

SIAM J. Matrix Anal. & Appl.

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show abstract

“…Chan and Li present a beautiful, constructive proof of the converse part of the Schur-Horn theorem [11]. Suppose that w w w and are N -dimensional, real vectors for which w w w .…”

Section: A a Numerically Stable Finite Algorithmmentioning

confidence: 99%

Finite-Step Algorithms for Constructing Optimal CDMA Signature Sequences

Tropp

Dhillon

Heath

2004

IEEE Trans. Inform. Theory

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Abstract-A description of optimal sequences for direct-spread codedivision multiple access (S-CDMA) is a byproduct of recent characterizations of the sum capacity. This correspondence restates the sequence design problem as an inverse singular value problem and shows that the problem can be solved with finite-step algorithms from matrix theory. It proposes a new one-sided algorithm that is numerically stable and faster than previous methods.Index Terms-Algorithms, code-division multiple access (CDMA), inverse eigenvalue problems, optimal sequences, sum capacity.

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“…Our proof differs from Horn's proof in two ways that (i) our proof is divided into two cases according to λ 1 = 0 and λ 1 = 0, and (ii) our induction technique is different. It is very much like Chan and Li's technique [1] (the same…”

mentioning

confidence: 96%