On the calculation of bounds for the spectrum of a symmetric matrix

Summary (translated from the Russian): "We present algorithms for the relatively fast, high-accuracy search for the extremal constants gamma_1 and gamma_2 ensuring the inequalities gamma_1 Dleq Aleqgamma_2 D in the operator sense for the large-scale square matrices A and D, where D is positive-definite. We give the results of numerical experiments on the determination of bounds for the spectrum of the discrete Laplace operator with zero boundary conditions in various domains, as well as Hilbert matrices of ninth order."