互惠条件

Compute reciprocal condition of square matrix in 1-norm

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Math Functions / Matrices and Linear Algebra / Matrix Operations

dspmtrx3

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

y = rcond(A) % Equivalent MATLAB code

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

where κ is the condition number (κ ≥ 1), andyis 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:

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

Generated code relies on thememcpyormemsetfunction (string.h) under certain conditions.

Introduced before R2006a