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Squeeze Theorems to Prove Convergence in Two Dimensions
Attend a seminar by Dr. Ziyad Sharawi, Associate Professor of Mathematics and Statistics.
Squeeze theorems (or comparison tests) are used at the calculus level to prove existence of limits or asymptotic behavior. In higher level courses like numerical analysis, squeeze theorems are used to prove convergence to a fixed point. Although the concept is simple, finding the right comparison is not a simple task. In this talk, we consider recurrence relations in one and two dimensions, and discuss some squeeze theorems that establish convergence to a steady state. The instrumental idea is to be able to use the fact that every bounded-monotonic sequence is convergent. Establishing monotonicity in two dimensions needs certain order, and one of the interesting techniques is to embed the recurrence relation into a higher dimensional one, then use squeeze theorems and convergence in high dimension to prove convergence in the original recurrence relation.