An Extension of Aronszajn’S Rule: Slicing the Spectrum for Intermediate Problems
Christopher Beattie · SIAM Journal on Numerical Analysis · 1987
We introduce an equivalent formulation of Aronszajn’s rule for the method of intermediate problems that provides more information of computational importance. The new formulation provides a mechanism for counting the number of intermediate problem eigenvalues in any given interval, thus allowing localization strategies to be developed analogous to Sturm sequence strategies used in polynomial root finding. Additionally, the relationship of the eigenvector-free estimation method of Goerisch with intermediate problems is clarified.