Consider a second order iterative scheme u(k+2) = Au(k+l) + Bu(k). Define a quadratic eigenvalue to be
Question:
det(λ2I - λA - B) = 0.
Prove that the system is asymptotically stable if and only if all its quadratic eigenvalues satisfy |λ| < 1. Look at the equivalent first order system and use Exercise 1.9.23b.
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The equivalent first order system v k1 Cv k for has coefficient matrix To compute ...View the full answer
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