for stability we consider the matrix iteration equation w(y+1) = ABw(y) + A (v) Consider the...

 

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for stability we consider the matrix iteration equation w(y+1) = ABw(y) + A (v) Consider the 0 method with 0 = 0. a) Find all the eigenvalues of W = = A-B b) Is it true that all eigenvalues of W are real and lying in (-1,1)? If yes please prove it, if no please provide an example = c) Is method with O unconditionally stable? If yes please prove it, if no, please provide detailed reasoning (and if there is a stability condition you can arrive at, please provide it) for stability we consider the matrix iteration equation w(y+1) = ABw(y) + A (v) Consider the 0 method with 0 = 0. a) Find all the eigenvalues of W = = A-B b) Is it true that all eigenvalues of W are real and lying in (-1,1)? If yes please prove it, if no please provide an example = c) Is method with O unconditionally stable? If yes please prove it, if no, please provide detailed reasoning (and if there is a stability condition you can arrive at, please provide it)