The binary scindage (in English binary splitting ) is a method of acceleration of the calculation of sums with terms rational S.
The binary scindage for example is used for the evaluation of hypergeometric series in rational points.
The basic principle of the binary scindage consists in recursively dividing the field of summation into small groups of rational to add, to simplify the sums of small groups (reduction with the same denominator, elimination of the common factors) and to reiterate on larger groups.
OperationThat is to say the sum
The scindage consists in dividing the interval '' B '' into two equal intervals: '' m '' and '' B '' (where m = is the medium of the segment) and to calculate recursively P ( has , B ) and Q ( has , B ) starting from P ( has , m ), P ( m , B ), Q ( has , m ) and Q ( m , B ).
When the two terminals of the interval of the subdivision '' J '' are sufficiently close, the calculation of P ( I , J ) and Q ( I , J ) is pj carried out directly starting from the pi… pj and qi… qj .
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