semiconvergent
A kind of fraction. If/,/ are successive convergents, then any fraction of the form/,…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.
Meaning
1 sensesA 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.
Origin
From semi- + convergent.From semi- + convergent.
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Forms
plural: semiconvergents| Singular | semiconvergent |
|---|---|
| Plural | semiconvergents |
regular