Sentence examples for the continued fraction from inspiring English sources

While approximations of the non-integer order Laplacian operator sα in terms of second order rational function using the continued fraction expansion method for the design of fractional order low pass Butterworth filters (FOLBFs) is recently reported in literature, however, such a design technique is non-optimal.

This paper uses the Continued Fraction Expansion (CFE) method for analog realization of fractional order differ-integrator and few special classes of fractional order (FO) controllers viz.

As each successive term is added, the continued fraction converges towards a single value.

The investigation into the structures of cascade systems was conducted by means of the software method for distributing the dynamic characteristics to the continued fraction based on graphs and structural numbers.

Qin gave an algorithm for this, using a sequence of quotients in searching for the greatest common divisor of a and b, which is also the sequence of convergents for the continued fraction for b/a.

If α is any irrational number, algebraic or not, there are infinitely many rational numbers p/q such that | p/q − α | < 1/q2 since the convergents of the continued fraction for α will suffice.

Open the "Continued Fractions" worksheet saved from the previous article, "How to Start Working with Continued Fractions", or whatever filename you saved it under.

To calculate the vibrational cross sections, we applied the multichannel version of the continued fractions method in the close-coupling scheme.

Basically, the three-term recurrence relation corresponds to the expressions for the numerators and denominators of this continued fraction (see Chapter IV in [3]), which were derived by Euler.

Obviously, the sequence is not a Cauchy sequence according to the norm, so the vectorial continued fraction (1.1) does not converge in norm.

Consequently, the vectorial continued fraction (1.1) converges according to the spectral seminorm to the value.