semiconvergent

Noun

 * 1)  A kind of fraction. If $$ \frac{h_{n-1} }{k_{n-1} } $$, $$ \frac{h_n}{k_n} $$ are successive convergents, then any fraction of the form $$ \frac{h_{n-1} + ah_n}{k_{n-1} + ak_n} $$, where a is a nonnegative integer and the numerators and denominators are between the n and n+1 terms inclusive, is a semiconvergent.
 * The semiconvergents to the continued fraction expansion of a real number include all the rational approximations which are better than any approximation with a smaller denominator.

Adjective

 * 1)  For which the limit $$ \lim_{k \to \infty} \bold T^k $$ exists.