What is "semiconvergent"

a. (context math of a matrix English) For which the limit $lim\_\{k\; to\; infty\}\; bold\; T^k$ exists. n. (context math English) 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.