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Question: Solution for 4x4 Algebraic Riccati Equation

Question:Solution for 4x4 Algebraic Riccati Equation

zoid 8 Maple
convert
October 23 2008
0
Hi, I am trying to find a general solution for a special case of the 4x4 Riccati Equation. My worksheet chugs for 5 hours and 2gigs of memory before crashing. Am I posing the problem incorrectly? Or will more memory help (and if so, how much memory)? > with(LinearAlgebra); > A := Matrix([[ZeroMatrix(2), IdentityMatrix(2)], [ZeroMatrix(2), Matrix(2, symbol = a)]]); > B := Matrix([[ZeroMatrix(2)], [Matrix(2, symbol = b)]]); > P := Matrix(4, 4, symbol = p); > S := evalm( Transpose(A)&*P + P&*A - P&*B&*Transpose(B)&*P + IdentityMatrix(4)); ... (Matrix has long entries --- they are quartic in a_ij, b_ij and p_ij) ... > solve(convert(S, set), convert(P, set)) (and then it chugs for 5 hours and 2gigs and crashes.) Any ideas? Thanks!
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