If the numerical rank of the matrix [AT BT]T is equal to (K+L), and (M - K - L) 0 then the generalized SVD is defined to be:
where U, V, and Q are orthogonal or unitary matrices, R is nonsingular upper triangular, [C]2 + [S]2 = [I], and
On exit, R is stored in A(1:K+L, N-K-L+1:N).
If the numerical rank of the matrix [AT BT]T is equal to (K+L), and (M - K - L) < 0 then the generalized SVD is defined to be:
On exit, R(1:M, K+L) is stored in A(1:M, N-K-L+1:N) and R(M+1:K+L, M+1:K+L) is stored in B(M-K+1:L, N+M-K-L+1:N).
|
A: |
2.0 4.0 12.0 |
0.0 12.0 20.0 |
0.0 0.0 24.0 |
|
B: |
2.0 4.0 12.0 |
0.0 6.0 10.0 |
0.0 0.0 8.0 |
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ALPHA: |
0.8944 0.9487 0.7071 |
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BETA: |
0.4472 0.3162 0.7071 |
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ALPHA(i) / BETA(i): |
2.0000 |
3.0000 |
1.0000 |
|