y^{(n)} = ƒ (x, y, y^{′}, y^{′′}, …, y^{(n−1)} ), α < x < b,

y^{(i)} (x_{j}) = y_{ij}, 0 ≤ i ≤ m_{j}, 1 ≤ j ≤ k − 1,

y*(i)* (x_{k}) + ∫ ^{d} _{c} py(x) dx=y_{ik}, 0 ≤ i ≤ m_{k}, ∑^{k} _{i=1} m_{i} = n,

with respect to the boundary data. We show that under certain conditions, partial derivatives of the solution y(x) of the boundary value problem with respect to the various boundary data exist and solve the associated variational equation along y(x).

]]>function. Our main results establish that optimization of quality-rather than quantity-when making a prediction has higher overall accuracy. ]]>