Description

The SVD Solver block solves the linear system AX=B, which can be overdetermined, underdetermined, or exactly determined. The system is solved by applying singular value decomposition (SVD) factorization to the M-by-N matrix A, at the A port. The input to the B port is the right side M-by-L matrix, B. The block treats length-M unoriented vector input as an M-by-1 matrix.

The output at the X port is the N-by-L matrix, X. X is chosen to minimize the sum of the squares of the elements of B-AX (the residual). When B is a vector, this solution minimizes the vector 2-norm of the residual. When B is a matrix, this solution minimizes the matrix Frobenius norm of the residual. In this case, the columns of X are the solutions to the L corresponding systems AX_k=B_k, where B_k is the kth column of B, and X_k is the kth column of X.

X is known as the minimum-norm-residual solution to AX=B. The minimum-norm-residual solution is unique for overdetermined and exactly determined linear systems, but it is not unique for underdetermined linear systems. Thus when the SVD Solver block is applied to an underdetermined system, the output X is chosen such that the number of nonzero entries in X is minimized.

Parameters

Supported Data Types

See Also

See Linear System Solvers for related information.