Reciprocal Condition

Compute reciprocal condition of square matrix in 1-norm

Library

Math Functions / Matrices and Linear Algebra / Matrix Operations

dspmtrx3

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Description

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

y = rcond(A)					% Equivalent MATLAB code

or

$$y=\frac{1}{\kappa }=\frac{1}{{\Vert A^{-1}\Vert }_1{\Vert A^{}\Vert }_1}$$

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

The matrix 1-norm, $${\Vert A\Vert }_1$$, is the maximum column-sum in the M-by-M matrix A.

$${\Vert A\Vert }_1=\stackrel{\max }{{\displaystyle 1\le j\le M}}{\displaystyle \sum _{i=1}^M\left|a_{ij}\right|}$$

For a 3-by-3 matrix:

References

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

Supported Data Types

• Double-precision floating point

• Single-precision floating point