LOCATING ROOTS OF A CERTAIN CLASS OF POLYNOMIALS
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We introduce a special class of real recurrent polynomials f_m (m ≥ 1) of degree m+1, with positive roots sm, which are decreasing as m increases. The first root s1, as well as the last one denoted by s∞ are expressed in closed form, and enclose all sm (m > 1). This technique is also used to find weaker than before [6] suffcient convergence conditions for some popular iterative processes converging to solutions of equations.
Abstract
We introduce a special class of real recurrent polynomials f_m (m ≥ 1) of degree m+1, with positive roots sm, which are decreasing as m increases. The first root s1, as well as the last one denoted by s∞ are expressed in closed form, and enclose all sm (m > 1). This technique is also used to find weaker than before [6] suffcient convergence conditions for some popular iterative processes converging to solutions of equations.
참고문헌 (9)
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