Square Root Function Forward Mode Theory
Keywords: square root function forward mode theory sqrt

| Prev | Next |  |  |  |  |  | sqrt_forward | Headings

Square Root Function Forward Mode Theory
If F ( x ) = x F ( x ) * F ( 1 ) ( x ) - 0 * F ( x ) = 1 / 2 and in the standard math function differential equation , A ( x ) = 0 , B ( x ) = F ( x ) , and D ( x ) = 1 / 2 . We use a , b , d , and z to denote the Taylor coefficients for A [ X ( t ) ] , B [ X ( t ) ] , D [ X ( t ) ] , and F [ X ( t ) ] respectively. It now follows from the general Taylor coefficients recursion formula that for j = 0 , 1 , … , z ( 0 ) = x ( 0 ) e ( j ) = d ( j ) + ∑ k = 0 j a ( j - k ) * z ( k ) = { 1 / 2 if j = 0 0 otherwise z ( j + 1 ) = 1 j + 1 1 b ( 0 ) (∑ k = 1 j + 1 k x ( k ) e ( j + 1 - k ) - ∑ k = 1 j k z ( k ) b ( j + 1 - k ) ) = 1 j + 1 1 z ( 0 ) (j + 1 2 x ( j + 1 ) - ∑ k = 1 j k z ( k ) z ( j + 1 - k ) )

Input File: omh/theory/sqrt_forward.omh