Improving Approximate Eigenvalues and Eigenvectors

by Arthur R. Robinson, (M.ASCE), Prof. of Civ. Engrg.; Univ. of Illinois, Urbana, IL,
John F. Harris, (A.M.ASCE), Assoc. Sr. Res. Engr.; General Motors Res. Lab., Warren, MI; formerly, Grad. Student, Dept. of Civ. Engrg., Univ. of Illinois, Urbana, IL,

Serial Information: Journal of the Engineering Mechanics Division, 1971, Vol. 97, Issue 2, Pg. 457-475

Document Type: Journal Paper


A numerical method is described for improving estimates for eigenvalues and eigenvectors of a wide class of operators, including those which arise in structural applications. The method, a modification of the Newton-Raphson technique, is applied to the solution of linear eigenvalue problems for systems with a finite number of degrees-of-freedom as well as for continuous systems. In addition, the extensions to cases of multiple eigenvalues and to problems involving nonlinear structural response are developed. Numerical results are presented for three examples. A fourth case dealing with nonlinear structural response is described briefly.

Subject Headings: Numerical methods | Eigenvalues | Case studies | Nonlinear response | Structural response | Nonlinear analysis | Linear functions

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