In practice, the linear approximation (above) works only over a small temperature range.

However, for weak fields, a linear approximation can be made.

However, this is really an artifact of the linear approximation.

For small changes in yield, the linear approximation will be reasonably good.

A linear approximation can be made to the metric in these circumstances.

If this is the same as the linear approximation.

Instead of working with full polynomials, we can use a linear approximation.

The derivative gives the best possible linear approximation, but this can be very different from the original function.

This is a natural inverse of the linear approximation to tetration.

But for large jumps in yield, the linear approximation will become very poor if convexity is high.

This has led to the investigation of higher order terms of the system size expansion that go beyond the linear approximation.

Elo devised a linear approximation to his full system.

This can be corrected by applying the linear approximation in the form:

If one were to make the linear approximation of, none of the effects under consideration would be obtained.

As a consequence, the linear approximation to f(x), which is used to pick the false position, does not improve in its quality.

The modified duration is a measure of the price sensitivity to yields and provides a linear approximation.

Duration is a linear approximation to the present-value profile.

In mathematics linearization refers to finding the linear approximation to a function at a given point.

The episode illustrates the use of linear approximation and the differential of a function.

If the temperature T does not vary too much, a linear approximation is typically used:

The tangent plane is the best linear approximation, or linearization, of a surface at a point.

There are also techniques for iteratively improving linear approximations (Matsui 1994).

It can be shown that - to a linear approximation - it is always possible to make the field traceless.

This linear transformation is the best linear approximation of the function F near the point p.

Up to changing variables, this is the statement that the function is the best linear approximation to f at a.