Stability of Roots of Polynomials Under Linear Combinations of Derivatives

作者：Curgus Branko^*; Mascioni Vania

来源：Constructive Approximation, 2010, 32(3): 523-541.

DOI：10.1007/s00365-009-9061-3

• Roots of polynomials
• Linear operators
• Minimum root separation

Let T = alpha(0)I + alpha(1)D + ... + alpha(n)D" , where D is the differentiation operator and alpha(0) not equal 0, and let f be a square-free polynomial with large minimum root separation. We prove that the roots of T f are close to the roots of f translated by -alpha(1)/alpha(0).

• 出版日期2010