Squaring the relative error corresponds precisely to doubling the number of significant digits, and hence explains the phenomenon above.

Square Root Curve Chart Actual % SqRtCurve

We want to solve the equation f(x) = 0. Newton gave a useful general recipe for solving equations of the form f(x) = 0. Say we have some approximation xk to a solution. He showed how to get a better …

Simplest version: \begin{array}{cols} row1 \\ row2 \\ . . . rowm \end{array} where cols includes one character [lrc] for each column (with optional characters | inserted for vertical lines) and rowj includes …

One very common and relatively quick method for find-ing the square root of a number is the Newton-Raphson method. Although this method is quick in terms of mathematics, it also requires extensive …

Abstract These notes for introductory scientific programming courses describe an implementation of the Cody-Waite algorithm for accurate computation of square roots, the simplest instance of the Fortran …

Example: Vector multiplier (VMUL) loads data from two vector registers, R1 and R2, each holding 4 double-precision numbers, concurrently performs 4 multiplications, and stores the results on vector …