Dictionary

semiconvergent en · ADJ

Etymology

From semi- + convergent.

Meanings

1. (not-comparable, of a matrix) For which the limit lim _(k→∞) bold Tᵏ exists.

semiconvergent en · NOUN

Etymology

From semi- + convergent.

Meanings

1. 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.

Forms