Variational equations for the eigenvalues and eigenvectors of nonsymmetric matrices

Kalaba, Robert E.; Spingarn, K.; Tesfatsion, Leigh

doi:10.1007/bf00935172

Cited by 27 publications

(20 citation statements)

References 2 publications

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“…References [29] and [30] provide an approach for developing the eigenvalue and eigenvector differential equation for the parameterized matrix . For any eigenvalue of , and corresponding eigenvector , the following relation is well known:…”

Section: Overview Of Current Methodsmentioning

confidence: 99%

“…A new eigenvalue-tracking approach [29], [30] for power system applications is proposed. This method involves a set of differential equations.…”

Section: Overview Of Current Methodsmentioning

confidence: 99%

“…If we apply the approach in [29] and [30] into the power system, (2.1) will become and are the eigenvalue and the right eigenvector that we want to trace. To preserve the sparsity, an extended eigenvector is defined as .…”

Section: A Oscillatory Stability Margin Identificationmentioning

confidence: 99%

See 2 more Smart Citations

Application of a Novel Eigenvalue Trajectory Tracing Method to Identify Both Oscillatory Stability Margin and Damping Margin

Wen¹,

Ajjarapu

2006

IEEE Trans. Power Syst.

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This paper is proposing an integration-based approach to trace a specific eigenvalue or a set of eigenvalues of a power system network. Indices are developed to identify critical eigenvalue to be traced for further analysis. This index takes into account the rate of change as well as the direction of movement. The rate of change is with respect to any parameter variation of interest. It finally provides information related to oscillatory stability and margin requirements to maintain a specific damping ratio. Eigenvalue and eigenvector sensitivities (with respect to any explicit/implicit parameters) are by-products of this approach.

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Section: Overview Of Current Methodsmentioning

confidence: 99%

“…A new eigenvalue-tracking approach [29], [30] for power system applications is proposed. This method involves a set of differential equations.…”

Section: Overview Of Current Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Application of a Novel Eigenvalue Trajectory Tracing Method to Identify Both Oscillatory Stability Margin and Damping Margin

Wen¹,

Ajjarapu

2006

IEEE Trans. Power Syst.

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“…PCA is a well-known transformation that herein provides a simple method of optimal transformation to distinguish the tissue types. After PCA training, the eigenvectors (Kalaba et al, 1981) are determined that represent the directions of maximum variance for the desired four classes. Then, given a test sample and projecting it to the trained eigenspace, we can compute the Mahalanobis distance (Duda et al, 2001) between the sample and each class.…”

Section: Introductionmentioning

confidence: 99%

Color‐based tumor tissue segmentation for the automated estimation of oral cancer parameters

Sun

Wang

Chang

et al. 2009

Microscopy Res & Technique

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This article presents an automatic color-based feature extraction system for parameter estimation of oral cancer from optical microscopic images. The system first reduces image-to-image variations by means of color normalization. We then construct a database which consists of typical cancer images. The color parameters extracted from this database are then used in automated online sampling from oral cancer images. Principal component analysis is subsequently used to divide the color features into four tissue types. Each pixel in the cancer image is then classified into the corresponding tissue types based on the Mahalanobis distance. The aforementioned procedures are all fully automated; in particular, the automated sampling step greatly reduces the need for intensive labor in manual sampling and training. Experiments reveal high levels of consistency among the results achieved using the manual, semiautomatic, and fully automatic methods. Parameter comparisons between the four cancer stages are conducted, and only the mean parameters between early and late cancer stages are statistically different. In summary, the proposed system provides a useful and convenient tool for automatic segmentation and evaluation for stained biopsy samples of oral cancer. This tool can also be modified and applied to other tissue images with similar staining conditions.

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“…It may also be possible to bypass the eigenvectors and directly treat the coefficients of the characteristic polynomial and the number of eigenvalues in any given region of the complex plane. (See [13,14,15] …”

mentioning

confidence: 99%

Complete comparative static differential equations

Kalaba

Tesfatsion

1981

Nonlinear Analysis: Theory, Methods & Applications

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Variational equations for the eigenvalues and eigenvectors of nonsymmetric matrices

Cited by 27 publications

References 2 publications

Application of a Novel Eigenvalue Trajectory Tracing Method to Identify Both Oscillatory Stability Margin and Damping Margin

Application of a Novel Eigenvalue Trajectory Tracing Method to Identify Both Oscillatory Stability Margin and Damping Margin

Color‐based tumor tissue segmentation for the automated estimation of oral cancer parameters

Complete comparative static differential equations

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