Meaning
Numerical sensitivity metrics quantify how much the output of a mathematical function changes relative to small perturbations in the input data. A high matrix condition number warns that a system of equations is nearly singular and that the resulting solution may be dominated by rounding errors. This value is used to assess the reliability of regression models and structural engineering simulations.
Stability Limit
Sensitivity of the output depends on the ratio of the largest singular value to the smallest. When the matrix condition number is large, the matrix is close to being singular. Small errors in the measurement of the input variables lead to huge variations in the resulting solution.
Inversion Accuracy
Stability of the inversion process is compromised when the condition number exceeds the reciprocal of the machine epsilon. In these cases, the matrix is impossible to invert accurately using standard floating point arithmetic. High values suggest that the data set contains redundant information which prevents a unique solution from being identified for the matrix condition number calculation.
The result becomes unreliable for predicting market trends if the underlying data is nearly singular.
Computational Cost
Performance of iterative solvers degrades as the condition number increases.
