New definition of multiple-root sensitivity

The sensitivity of a simple root of a polynominal is finite and well defined. For a multiple root, however, the existing definition becomes infinite, even when the root displacements remain finite. In this letter, a well behaved function is proposed to define a multiple-root sensitivity. It is also shown that the new definition, which degenerates to the conventional definition under a special condition, is a meaningful measure of actual root displacements.