Let the weight function w be symmetric with respect to the center c of (a, b), i.e. w(x) = w(2c - x) for all x belongs to (a, b). show that if f is also symmetric with respect to the center f(x) = f(2c - x) then the polynomial Pn that is the best least approximation to f is also symmetric.
any suggestions??? thanks a bunch
2006-11-27 16:16:19 · 2 answers · asked by Nate 3 in Science & Mathematics ➔ Mathematics
if linear or quadratic (or even) it (Pn) would be symmetric.
2006-12-01 06:43:26 · answer #1 · answered by mr green 4 · 0⤊ 0⤋
The Rhind Mathematical Papyrus is a reproduction from 1650 BCE of a outstanding until at last now artwork and shows us how the Egyptians extracted sq. roots. In historic India, the very fact of theoretical and utilized components of sq. and sq. root replaced into a minimum of as previous because of the fact the Sulba Sutras, dated around 800-500 B.C. (probable plenty until at last now). a manner for discovering very stable approximations to the sq. roots of two and 3 are given interior the Baudhayana Sulba Sutra. Aryabhata interior the Aryabhatiya (area 2.4), has given a manner for discovering the sq. root of numbers having many digits. D.E. Smith in history of arithmetic, says, relating to the present day difficulty in Europe: "In Europe those procedures (for discovering out the sq. and sq. root) did now no longer look until at last now Cataneo (1546). He gave the strategy of Aryabhata for figuring out the sq. root".
2016-12-10 17:29:58 · answer #2 · answered by ? 4 · 0⤊ 0⤋