A sequence {p) is said to be superlinearly convergentto p if .. \Pn+\ - P\ hm = 0. "^0 Ipn - pi a. Show thatif p > p of order a for a > 1, then {p) is superlinearly convergent to p. b. Show that p,, is superlinearly convergent to 0 but does not converge to 0 of ordera for any a > 1.

MATH 340 – INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS What We Covered: April 4 1. Course Content – Chapter 9: Linear Systems with Constant Coefficients a. Section 9.6: The Exponential of a Matrix 1 2 i. The exponential of the matrix A is defined to be = 2! + + 1 3 ∞ 1 3! +...= ∑=0! ii. Proposition: Suppose A is an nxn matrix 1. Then =