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Noncommutative Continued Fractions
SIAM Journal on Mathematical Analysis, 1971A number of theorems are proved concerning the convergence of continued fractions whose entries are linear operators on a Banach space. These theorems are analogues of some of the well-known results for ordinary continued fractions.
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Continued Logarithms and Associated Continued Fractions
Experimental Mathematics, 2016ABSTRACTWe investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical
Jonathan M. Borwein +3 more
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On Recurring Continued Fractions
The Mathematical Gazette, 1934Notation . By ( x/y, X/Y ) = a 1 . a 2 a 3 … are let it be understood that after a vulgar fraction
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Proceedings 15th IEEE Symposium on Computer Arithmetic. ARITH-15 2001, 2002
The leading seven terms of a continued fraction were investigated and used to perform on-line arithmetic. A new way to give interval for continued fractions was analyzed. Three important properties were identified for a continued fraction representation of real numbers.
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The leading seven terms of a continued fraction were investigated and used to perform on-line arithmetic. A new way to give interval for continued fractions was analyzed. Three important properties were identified for a continued fraction representation of real numbers.
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The computational complexity of continued fractions
Proceedings of the fourth ACM symposium on Symbolic and algebraic computation - SYMSAC '81, 1981The paper deals with the complexity of expanding a quolynomial into a continued fraction and shows that the Knuth-Schönage algorithm is essentially optimal with respect to the number of multiplications/divisions used, uniformly in the inputs. The problem consists in computing, given a pair \((A_ 1,A_ 2)\) of polynomials in the indeterminate x over a ...
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Branched Continued Fraction Expansions of Horn’s Hypergeometric Function H3 Ratios
Mathematics, 2021Tamara Antonova +2 more
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Beta-expansion and continued fraction expansion
Journal of Mathematical Analysis and Applications, 2008Jun Wu, Bing Li
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