A Two-Dimensional Bisection Method for Solving Two-Parameter Eigenvalue Problems
Xingzhi Ji · SIAM Journal on Matrix Analysis and Applications · 1992
It has long been known that separation of variables can be applied to the Helmholtz equation in 11 three-dimensional coordinate systems. As a result, a multiparameter eigenvalue problem is formed. In this paper, the well-known bisection method for ordinary eigenvalue problems is generalized to a special class of discrete two-parameter eigenvalue problems. The range of the real roots of the problem is discussed and some numerical results are given.