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The elements of an arithmetico-geometric sequence () are the products of the elements of an arithmetic progression (in blue) with initial value and common difference , = + (), with the corresponding elements of a geometric progression (in green) with initial value and common ratio , =, so that [4]
On an expression or formula calculator, one types in an expression and then presses a key, such as "=" or "Enter", to evaluate the expression. [ 4 ] [ 5 ] [ 6 ] There are various systems for typing in an expression, as described below.
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
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In order of increasing accuracy, they are: (+ + + +), (maximum error: 5 × 10 −4) where a 1 = 0.278393 , a 2 = 0.230389 , a 3 = 0.000972 , a 4 = 0.078108 erf x ≈ 1 − ( a 1 t + a 2 t 2 + a 3 t 3 ) e − x 2 , t = 1 1 + p x , x ≥ 0 {\displaystyle \operatorname {erf} x\approx 1-\left(a_{1}t+a_{2}t^{2}+a_{3}t^{3}\right)e^{-x^{2 ...
Suppose we have a continuous differential equation ′ = (,), =, and we wish to compute an approximation of the true solution () at discrete time steps ,, …,.For simplicity, assume the time steps are equally spaced:
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
In computing, a roundoff error, [1] also called rounding error, [2] is the difference between the result produced by a given algorithm using exact arithmetic and the result produced by the same algorithm using finite-precision, rounded arithmetic. [3]