Abstract
We suggest an approximate method for evaluating functions of a linear pencil ℒ(λ) = λA — B with self-adjoint operator coefficients A and B. It is based on the calculation of a special rational function of ℒ. We assume that the operator A is bounded and positive definite, and the operator B can be unbounded. The estimates of the approximation error are obtained. As an application, an approximate method for calculating the impulse response of a linear differential equation Ax′ = Bx + g(t) is given. The suggested approach can be used in remodeling of the complicated systems.
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