DSP Blockset

SVD Solver

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 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. 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 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.

Dialog Box

Supported Data Types

• Double-precision floating point
• Single-precision floating point

To learn how to convert your data types 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.

Submatrix

Time Scope