## semiconvergent

Noun

(*plural* semiconvergents)

- (mathematics) A kind of fraction. If , are successive convergents, then any fraction of the form , 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

(*not comparable*)

- (mathematics, of a matrix) For which the limit exists.

Origin

*semi-* + *convergent*