The circumference of a sphere is measured to be 24 cm, with a possible error of 0.25 cm. Use the differential \(dV\) to estimate the maximum error in the calculated ...

\(\ds dV=\frac{72}{\pi^2}\text{.}\) Observe that \(\ds dr=\frac{1}{8\pi}\text{.}\) Observe that \(\Delta A=A(s+\Delta s)-A(s)=2s\Delta s+(\Delta s)^2\) and \(dA=2s ...

For over three centuries, researchers have relied on a powerful algorithm developed by Isaac Newton to tackle complex problems in logistics, finance, computer vision, and even pure math. This simple ...

If Newton's method is employed to find a root of a map from a Banach space into itself and the derivative is singular at that root, linear convergence of the Newton sequence to the root is the best ...

This MATLAB program implements a table lookup approximation of the function arcsin(x) for x in the range [0, π/4]. The approximation is achieved using inverse interpolation with cubic splines followed ...

The variational inequality formulation provides a mechanism for determining both the option value and the early exercise curve implicitly (Jaillet, Lamberton and Lapeyre, 1990). Standard ...

SIAM Journal on Numerical Analysis, Vol. 20, No. 2 (Apr., 1983), pp. 296-314 (19 pages) If Newton's method is employed to find a root of a map from a Banach space into itself and the derivative is ...