continued_fraction

continued_fraction, a MATLAB code which implements some simple algorithms for dealing with simple and generalized continued fractions.

Mathematically, continued fractions are infinite sums. In general, they are treated computationally as finite sums. Here we will assume that all such sums terminate at index N.

A simple continued fraction (SCF) is a representation of a number R as:

        R = A0 + 1 / ( A1 + 1 / ( A2 + 1 / ( A3 + ... + 1 / AN )...)))
      

A generalized continued fraction (GCF) is a representation of a number R as:

        R = A0 + B1 / ( A1 + B2 / ( A2 + B3 / ( A3 + ... + BN / AN )...)))
      

For either form of continued fraction, there are two tasks:

1. Given a value R, determine an N-term SCF or GCF which is equal to, or approximates, R.
2. Given the coefficients of an SCF or GCF, determine the sequence of rational values represented by computing the partial sums. The final sum is the value R.

Licensing:

The computer code and data files made available on this web page are distributed under the MIT license

Languages:

continued_fraction is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version and.

Related Software and Data:

continued_fraction_test

subset, a MATLAB code which enumerates, generates, randomizes, ranks and unranks combinatorial objects including combinations, compositions, Gray codes, index sets, partitions, permutations, polynomials, subsets, and Young tables. Backtracking routines are included to solve some combinatorial problems. Some routines for continued fractions are included.

Reference:

1. Norman Richert,
   Strang's Strange Figures,
   American Mathematical Monthly,
   Volume 99, Number 2, February 1992, pages 101-107.

Source Code:

• i4cf_evaluate.m, evaluates a continued fraction with I4 entries.
• i4scf_evaluate.m, evaluates a simple continued fraction with I4 entries.
• i4vec_print.m, prints an I4VEC.
• r8_to_i4scf.m, approximates an R8 with an I4 simple continued fraction.
• r8cf_evaluate.m, evaluates a continued fraction with R8 entries.
• r8scf_evaluate.m, evaluates a simple continued fraction with R8 entries.
• r8vec_print.m, prints an R8VEC.