Introduction
The Weierstrass approximation theorem states that every continuous function f(x) defined on an interval can be uniformly approximated as closely as desired by a polynomial function Pn(x) of degree ≤ n, i.e.,
Interpolation at equidistant points is a natural and well-known approach to construct approximating polynomials. Runge's phenomenon demonstrates, however, that interpolation can easily result in divergent approximations.
Read more about this topic: Runge's Phenomenon
Famous quotes containing the word introduction:
“Do you suppose I could buy back my introduction to you?”
—S.J. Perelman, U.S. screenwriter, Arthur Sheekman, Will Johnstone, and Norman Z. McLeod. Groucho Marx, Monkey Business, a wisecrack made to his fellow stowaway Chico Marx (1931)
“The role of the stepmother is the most difficult of all, because you can’t ever just be. You’re constantly being tested—by the children, the neighbors, your husband, the relatives, old friends who knew the children’s parents in their first marriage, and by yourself.”
—Anonymous Stepparent. Making It as a Stepparent, by Claire Berman, introduction (1980, repr. 1986)
“Such is oftenest the young man’s introduction to the forest, and the most original part of himself. He goes thither at first as a hunter and fisher, until at last, if he has the seeds of a better life in him, he distinguishes his proper objects, as a poet or naturalist it may be, and leaves the gun and fish-pole behind. The mass of men are still and always young in this respect.”
—Henry David Thoreau (1817–1862)