Direct Approximation of a Function or Its Inverse (cont)
Exploit low-cost Dynamic Random Access Memory (DRAM).
Use piecewise linear approximations for most functions.
- By far the most efficient approach for a fixed accuracy criterion
- Maximum flexibility in efficiency vs. accuracy tradeoffs
For a function f(x) defined on an interval [a, b], form a lattice of N+1 equally spaced points xi with lattice spacing ? = (b - a) / N.
f(x) is approximated by Ai + Bix on the i th interval using prestored coefficients Ai and Bi.
The local approximation can be interpolative, use least squares, or any other local approximation method.
For a given x, the value of i is given by i = greatest integer < (x / ?).
Computation cost is approximately two multiplies, an add, and the retrieval of Ai and Bi.
Accuracy is achieved with �large� i.