Condition Number of a Matrix and Methods of its Evaluation
Abstract
A system of linear algebraic equations Ax = b is considered. The condition number of the matrix A is introduced. It is shown to be a very important matrix characteristic, since it is the main indicator of the stability of the solution of the system, a measure of the sensitivity of the system with respect to errors in the elements of matrix A and components of vector b. The greater the condition number, the stronger this effect will be and the more unstable will be the process of finding the solution of the linear system. It is shown that the condition number o f a matrix does not depend on the value of its determinant. Methods are proposed to calculate or estimate this important characteristic.
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References
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