| DSP Blockset | |
Solve the equation AX=B using singular value decomposition.
Library
Math Functions / Matrices and Linear Algebra / Linear System Solvers
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 SVD factorization to the M-by-N matrix, A, at the A port. The input to the B port is the right hand-side M-by-L matrix, B. A length-M 1-D vector input at either port is treated as an M-by-1 matrix.
The output at the x port is the N-by-L matrix, X. X is always sample based, and is chosen to minimize the sum of the squares of the elements of B-AX. When B is a vector, this solution minimizes the vector 2-norm of the residual (B-AX is 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 AXk=Bk, where Bk is the kth column of B, and Xk 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 is applied to an underdetermined system, the output X is chosen such that the number of nonzero entries in X is minimized.
Dialog Box
Supported Data Types
To learn how to convert to the above data types in MATLAB and Simulink, see Supported Data Types and How to Convert to Them.
See Also
| Autocorrelation LPC |
DSP Blockset |
| Cholesky Solver |
DSP Blockset |
| LDL Solver |
DSP Blockset |
| Levinson-Durbin |
DSP Blockset |
| LU Inverse |
DSP Blockset |
| Pseudoinverse |
DSP Blockset |
| QR Solver |
DSP Blockset |
| Singular Value Decomposition |
DSP Blockset |
See Solving Linear Systems for related information. Also see Linear System Solvers for a list of all the blocks in the Linear System Solvers library.
| | Submatrix | Time Scope | |
