From which we have (a1 + a2 + a3 + a4) D+a5d-(1-A) (B1 + 32 +33 +34) D² = (1 - A) 35 Dd (5.32) and (a₁ + a2 + a3 + a4) d+a5D-(1-A) (B₁ + B2 + B3+ B4) d² = (1 - A) 5 Dd (5.33) From (5.32) and (5.33), we obtain (d-D) {[(a1 + a2 + a3 + a4) - a5] - (1 - A) (B1 + B2+ B3 + B4) (d+ D)} = 0. (5.34) Since A 1 and a5 2 (a1 + a2 + a3 + a4), we deduce from (5.34) that D = d. It follows by Theorem 2, that y of Eq. (1.1) is a global attractor.
From which we have (a1 + a2 + a3 + a4) D+a5d-(1-A) (B1 + 32 +33 +34) D² = (1 - A) 35 Dd (5.32) and (a₁ + a2 + a3 + a4) d+a5D-(1-A) (B₁ + B2 + B3+ B4) d² = (1 - A) 5 Dd (5.33) From (5.32) and (5.33), we obtain (d-D) {[(a1 + a2 + a3 + a4) - a5] - (1 - A) (B1 + B2+ B3 + B4) (d+ D)} = 0. (5.34) Since A 1 and a5 2 (a1 + a2 + a3 + a4), we deduce from (5.34) that D = d. It follows by Theorem 2, that y of Eq. (1.1) is a global attractor.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.2: Norms And Distance Functions
Problem 44EQ
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