Firstly, which computational phenomena can we model naturally using differential operators and Taylor expansion
Often, some property must be sacrificed to gain another.
is employed to linearize the nonlinear confluent hypergeometric function.
The key point is the use of a Taylor expansion
, at an appropriate point of the integration interval, of a certain factor of the integrand that is independent of the variable z.
By this, (19), and Taylor expansion
, we have from [9, (2.5)] that
In this paper, we revise the sparse matrix model by the one-order Taylor expansion
and propose the joint sparse matrix model.
The function is so nice; we can just use the Taylor expansion
around a = 0.
So, we resort to the Taylor expansion
method to solve the problem approximately.
However, this work proposes a Direct Pade(DP) modification oriented to reduce this algebraic operation by means of the Taylor expansion
of the rational function.
For small accelerations, using the first few terms of the Taylor expansion
, this time dilation expression can be written as
Each function g [member of] H has the Taylor expansion
g(z) = [[summation].sup.[infinity].sub.n-0] [a.sub.n][z.sup.n] in D and consequently, we have g'(z) = [[summation].sup.[infinity].sub.n-0] [na.sub.n][z.sup.n-1].
It is based on a first-order Taylor expansion
of the limit state function, at the mean values of the random variables, avoiding the need for solving an optimization problem to locate the most probable point (MPP).
TM calculations are carried out by using standard operations over polynomials or, whenever a nonlinear operator occurs, by the rules of Taylor expansion
. The interval remainder is propagated and updated by means of Taylor remainder theory and IA.