09 taylor models proof that arithmetic operation perforrmed with floatin point arithmetic provide guaranteed results n revol
09 taylor models proof that arithmetic operation perforrmed with floatin point arithmetic provide guaranteed results n revol
. - 18 N. Revol
Taylor models: proof that arithmetic
operations performed with floating -point
arithmetic provide guaranteed results
Nathalie Revol INRIA,. 11 N. Revol
Taylor models: notations
coefficients of the polynomial: a
i
, 1 ≤ i ≤ p (floating -point numbers)
I interval containing the Lagrange remainder,
taylor model and floating point arithmetic proof
. in
this paper provide guaranteed bounds even if they compute using floating -point operations
only.
3.2. Taylor models in COSY and IEEE-754 floating -point. (even), rounding to +∞, rounding to −∞ and rounding to 0. With directed
rounding modes,fl(x) is chosen asthe floating -point numberin the indicateddirection.
08 TAYLOR MODELS AND OTHER VALIDATED FUNCTIONAL INCLUDING METHOD MAKINO & m BERZ
. order
n and dim ension v is represented b y a collection of nonzero floating point
coefficients a
i
, as w ell a s two coding integers n
i,1
and n
i,2
that contain
uniqu. whichisexecutedinoutwardroundedinterval
arithme tic.
In trinsic Functions. All intrinsic functions can be expressed as
linear combinations of monom ials of Ta ylor models, p lus an interval
remainder
From interval analysis to taylor models an overview lohner
. arithmetic operation is automatically enclosed in a floating -point interval, including
roundoff errors. For example, sum and difference of two floating point intervals
X. calculated with two basic arithmetic operations between the endpoints of the intervals
X and Y , where
, denote operations with downward or upward rounding,
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