6533b7ddfe1ef96bd1273cb2

RESEARCH PRODUCT

Lower bounds for eigenvalues of a quadratic form relative to a positive quadratic form

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Abstract : A method is presented for the calculation of lower bounds to eigenvalues of operators that arise from variational problems for one quadratic form relative to a positive definite quadratic form. Eigenvalue problems of this kind occur, for example, in the theory of buckling of continuous linear elastic systems. The technique used is a modification of one introduced earlier, (1) sections II and IVB, for the determination of lower bounds to eigenvalues of semi-bounded self-adjoint operators. Other methods for the latter problem can be carried over without essential changes. The particular difficulty in the case we consider is that some operators which enter the calculation for the lower bounds are not generally known explicitly. Lower bound method is formulated for the problem considered here. Section IV develops the modification of the theory developed to show how it yields lower bounds. (Author)