Sollya User's Manual

Name:

taylorrecursions controls the number of recursion steps when applying Taylor's rule.

Library names:

void sollya_lib_set_taylorrecursions_and_print(sollya_obj_t) void sollya_lib_set_taylorrecursions(sollya_obj_t) sollya_obj_t sollya_lib_get_taylorrecursions()

Usage:

taylorrecursions = n : integer -> void taylorrecursions = n ! : integer -> void taylorrecursions : integer

Parameters:

n represents the number of recursions

Description:

taylorrecursions is a global variable. Its value represents the number of steps of recursion that are used when applying Taylor's rule. This rule is applied by the interval evaluator present in the core of Sollya (and particularly visible in commands like infnorm).
To improve the quality of an interval evaluation of a function f, in particular when there are problems of decorrelation), the evaluator of Sollya uses Taylor's rule: f([a,b]) C f(m) + [a-m, b-m]*f'([a,b]) where m=(a+b)/2. This rule can be applied recursively. The number of step in this recursion process is controlled by taylorrecursions.
Setting taylorrecursions to 0 makes Sollya use this rule only once; setting it to 1 makes Sollya use the rule twice, and so on. In particular: the rule is always applied at least once.

Example 1:

   > f=exp(x);
   > p=remez(f,3,[0;1]);
   > taylorrecursions=0;
   The number of recursions for Taylor evaluation has been set to 0.
   > evaluate(f-p, [0;1]);
   [-0.46839364816268368775174657814112460243249079671039;0.46947781754646820647293019728402934746974652584671]
   > taylorrecursions=1;
   The number of recursions for Taylor evaluation has been set to 1.
   > evaluate(f-p, [0;1]);
   [-0.138131114954063839905475752120786856031651747712954;0.13921528433784835862665937126369160106890747684927]

See also: hopitalrecursions, evaluate, infnorm

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