منابع مشابه
continued fraction ∗
We use a continued fraction expansion of the sign-function in order to obtain a five dimensional formulation of the overlap lattice Dirac operator. Within this formulation the inverse of the overlap operator can be calculated by a single Krylov space method where nested conjugate gradient procedures are avoided. We show that the five dimensional linear system can be made well conditioned using ...
متن کاملThe Szekeres Multidimensional Continued Fraction
In his paper "Multidimensional continued fractions" {Ann. Univ. Sei. Budapest. EOtvOs Sect. Math., y. 13, 1970, pp. 113-140), G. Szekeres introduced a new higher dimensional analogue of the ordinary continued fraction expansion of a single real number. The Szekeres algorithm associates with each fc-tuple (a»,..., ak) of real numbers (satisfying 0 < a< 1) a sequence bx, b2,... of positive intege...
متن کاملThe Random Continued Fraction Transformation
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the Rényi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
متن کاملThe Hurwitz Complex Continued Fraction
The Hurwitz complex continued fraction algorithm generates Gaussian rational approximations to an arbitrary complex number α by way of a sequence (a0, a1, . . .) of Gaussian integers determined by a0 = [α], z0 = α − a0, (where [u] denotes the Gaussian integer nearest u) and for j ≥ 1, aj = [1/zj−1], zj = 1/zj−1−aj . The rational approximations are the finite continued fractions [a0; a1, . . . ,...
متن کاملA q-CONTINUED FRACTION
Let a, b, c, d be complex numbers with d 6= 0 and |q| < 1. Define H1(a, b, c, d, q) := 1 1 + −abq + c (a + b)q + d + · · · + −abq + cq (a + b)qn+1 + d + · · · . We show that H1(a, b, c, d, q) converges and 1 H1(a, b, c, d, q) − 1 = c − abq d + aq P∞ j=0 (b/d)(−c/bd)j q (q)j(−aq/d)j P∞ j=0 (b/d)(−c/bd)j q (q)j(−aq/d)j . We then use this result to deduce various corollaries, including the followi...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(99)00033-3