A more practical way to generalize Filon's method for (1.2) is to approximate g(x) by a spline s(x) and then integrate analytically
It is convenient in both theory and practice to approximate the complex integral and then obtain trigonometric integrals from the real and imaginary parts of the result,
The generalized Filon methods we consider for (1.2) approximate the integral with the exact integral of the approximating problem (1.4).
If we write g(x) = wG(x), the accuracy of the method depends on how well we approximate G(x) because the generalized Filon approach deals analytically with the effects of large w.
If both approximations on a subinterval are sufficiently accurate, the approximate integral (3.1) is formed as described in Section 4.1.
For the test (3.2) we can obtain a reasonable estimate of the general size of F(x) for "free" by applying Simpson's rule on each [[x.sub.m], [x.sub.m+1]] to approximate
Sethe's killing of Beloved remains an inconceivable gesture whose meaning Beloved spends its entire length trying to approximate
. In Schoolteacher's nephew's reaction to Sethe's killing in the woodshed, Morrison highlights the mistaken meanings derived from decontextualized judgments:
In short, assume all but epistemic forms of realism for scientific theories; we leave it open whether we can justify belief in the truth or approximate truth of the U- statements of theories.
Since I will later use the empirical adequacy of theories as part of a test for the approximate truth of their U-statements, evidence must so connect to theory that it truly tests it and can weakly confirm it; the theory can only be true given certain evidence.
Third, the resemblances must exceed the theories making the same O- predictions, else truth (or approximate truth) is empirical adequacy, contradicting the realist view that truth is independent of our epistemic limitations.
The inference won't be ampliative (won't go beyond the empirical evidence) if approximate truth follows trivially on empirical adequacy merely because the latter is a component in the truth, any A-theory (plus background information) logically containing such a component and so being ipso facto truish.
The details do not matter here, only that he relates the approximate truth of a theory to its truth- conditions.