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Error bounds on the eigenvalues of a linearized dynamic stiffness matrix

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Error bounds on the eigenvalues of a linearized dynamic stiffness matrix. / Ye, J Q .
In: Communications in Numerical Methods in Engineering, Vol. 14, No. 4, 04.1998, p. 305-312.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Ye, JQ 1998, 'Error bounds on the eigenvalues of a linearized dynamic stiffness matrix', Communications in Numerical Methods in Engineering, vol. 14, no. 4, pp. 305-312. https://doi.org/10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4

APA

Ye, J. Q. (1998). Error bounds on the eigenvalues of a linearized dynamic stiffness matrix. Communications in Numerical Methods in Engineering, 14(4), 305-312. https://doi.org/10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4

Vancouver

Ye JQ. Error bounds on the eigenvalues of a linearized dynamic stiffness matrix. Communications in Numerical Methods in Engineering. 1998 Apr;14(4):305-312. doi: 10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4

Author

Ye, J Q . / Error bounds on the eigenvalues of a linearized dynamic stiffness matrix. In: Communications in Numerical Methods in Engineering. 1998 ; Vol. 14, No. 4. pp. 305-312.

Bibtex

@article{0357407f6a984f90b2bdce43d6c8a089,
title = "Error bounds on the eigenvalues of a linearized dynamic stiffness matrix",
abstract = "In connection with previously published work, this paper presents further results about the bounding properties of eigenvalues provided by a linear eigenmatrix formulation A - lambda B. The linear eigenmatrix is formed by expressing the elements of a non-linear dynamic stiffness matrix, K(lambda), as linear functions of the eigenparameter lambda. This is achieved by choosing two fixed values of the eigenparameter and calculating K(lambda) at these two values. The eigenvalues of A - lambda B provide error bounds on the exact eigenvalues of the non-linear eigenmatrix if the two fixed values chosen are below the lowest pole of K(lambda). Choosing two identical fixed values, the error bounds on the exact eigenvalues provided by traditional linearization techniques are found as special cases. (C) 1998 John Wiley & Sons, Ltd.",
keywords = "error bound, non-linear eigenvalue, linearization, dynamic stiffness matrix, matrix pencil",
author = "Ye, {J Q}",
year = "1998",
month = apr,
doi = "10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4",
language = "English",
volume = "14",
pages = "305--312",
journal = "Communications in Numerical Methods in Engineering",
issn = "1069-8299",
publisher = "John Wiley and Sons Inc.",
number = "4",

}

RIS

TY - JOUR

T1 - Error bounds on the eigenvalues of a linearized dynamic stiffness matrix

AU - Ye, J Q

PY - 1998/4

Y1 - 1998/4

N2 - In connection with previously published work, this paper presents further results about the bounding properties of eigenvalues provided by a linear eigenmatrix formulation A - lambda B. The linear eigenmatrix is formed by expressing the elements of a non-linear dynamic stiffness matrix, K(lambda), as linear functions of the eigenparameter lambda. This is achieved by choosing two fixed values of the eigenparameter and calculating K(lambda) at these two values. The eigenvalues of A - lambda B provide error bounds on the exact eigenvalues of the non-linear eigenmatrix if the two fixed values chosen are below the lowest pole of K(lambda). Choosing two identical fixed values, the error bounds on the exact eigenvalues provided by traditional linearization techniques are found as special cases. (C) 1998 John Wiley & Sons, Ltd.

AB - In connection with previously published work, this paper presents further results about the bounding properties of eigenvalues provided by a linear eigenmatrix formulation A - lambda B. The linear eigenmatrix is formed by expressing the elements of a non-linear dynamic stiffness matrix, K(lambda), as linear functions of the eigenparameter lambda. This is achieved by choosing two fixed values of the eigenparameter and calculating K(lambda) at these two values. The eigenvalues of A - lambda B provide error bounds on the exact eigenvalues of the non-linear eigenmatrix if the two fixed values chosen are below the lowest pole of K(lambda). Choosing two identical fixed values, the error bounds on the exact eigenvalues provided by traditional linearization techniques are found as special cases. (C) 1998 John Wiley & Sons, Ltd.

KW - error bound

KW - non-linear eigenvalue

KW - linearization

KW - dynamic stiffness matrix

KW - matrix pencil

U2 - 10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4

DO - 10.1002/(SICI)1099-0887(199804)14:4<305::AID-CNM145>3.0.CO;2-4

M3 - Journal article

VL - 14

SP - 305

EP - 312

JO - Communications in Numerical Methods in Engineering

JF - Communications in Numerical Methods in Engineering

SN - 1069-8299

IS - 4

ER -