Reciprocal Condition

Compute reciprocal condition of square matrix in 1-norm

Libraries:
DSP System Toolbox / Math Functions / Matrices and Linear Algebra / Matrix Operations

Description

The Reciprocal Condition block computes the reciprocal of the condition number for a square input matrix A.

Here is the equivalent MATLAB^® code.

y = rcond(A)

$y = \frac{1}{κ} = \frac{1}{{‖ A^{- 1} ‖}_{1} {‖ A^{} ‖}_{1}},$

where κ is the condition number (κ ≥ 1), and y is the scalar output (0 ≤ y < 1).

The matrix 1-norm, ${‖ A ‖}_{1}$ , is the maximum column-sum in the M-by-M matrix A.

${‖ A ‖}_{1} = \overset{\max}{1 \leq j \leq M} \sum_{i = 1}^{M} | a_{i j} |$

For a 3-by-3 matrix:

Specify the input matrix as a square matrix.

Data Types: single | double

Reciprocal of the condition number for a square input matrix A, returned as a scalar.

If input is well conditioned, the output is near 1.0. If input is badly conditioned, the output is near 0.0.

Data Types: single | double

[1] Golub, G. H., and C. F. Van Loan. Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

Generated code relies on the memcpy or memset function (string.h) under certain conditions.

Introduced before R2006a