A GENERATION OF A DETERMINANTAL FAMILY OF ITERATION FUNCTIONS AND ITS CHARACTERIZATIONS
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Iteration functions Km(z) and Um(z) ; m ≥ 2 are de- fined recursively using the determinant of a matrix. We show that the fixed-iterations of Km(z) and Um(z) converge to a simple zero with order of convergence m and give closed form expansions of Km(z) and Um(z): To show the convergence, we derive a recursion formula for Lm and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is Lm(z)=(f¹)m, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.
Abstract
Iteration functions Km(z) and Um(z) ; m ≥ 2 are de- fined recursively using the determinant of a matrix. We show that the fixed-iterations of Km(z) and Um(z) converge to a simple zero with order of convergence m and give closed form expansions of Km(z) and Um(z): To show the convergence, we derive a recursion formula for Lm and then apply the idea of Ford or Pomentale. We also find a Toeplitz matrix whose determinant is Lm(z)=(f¹)m, and then we adapt the well-known results of Gerlach and Kalantari et.al. to give closed form expansions.
참고문헌 (11)
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