Definition of "semiconvergent" in English

noun

1. (mathematics) A kind of fraction. If (h_n-1)/(k_n-1), (h_n)/(k_n) are successive convergents, then any fraction of the form (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. (mathematics, of a matrix) For which the limit lim _(k→∞) bold Tᵏ exists.