semiconvergent

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Continued fraction

Wikipedia

English Wikipedia has an article on:

Convergent matrix

Wikipedia

From semi- +‎ convergent.

semiconvergent (plural semiconvergents)

(mathematics) 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.

semiconvergent (not comparable)

(mathematics, of a matrix) For which the limit $\lim _{k\to \infty }{\mathbf {T}}^{k}$ exists.