Re: "Cascaded sums"?
- To: mathgroup at smc.vnet.net
- Subject: [mg59220] Re: "Cascaded sums"?
- From: "Jens-Peer Kuska" <kuska at informatik.uni-leipzig.de>
- Date: Tue, 2 Aug 2005 00:42:50 -0400 (EDT)
- Organization: Uni Leipzig
- References: <dckb96$o4j$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Hi, it is called Horner schema in your example with respect to a. And it is used to optimize the evaluation of polynomials by a computer. The standard package <<Algebra`Horner` implement it. Its advantage is, that it reduce the numerical errors because a*x^4+b*x^3+c*x^2+d*x+e will add a x^4*a (that may be large compared with b*x^3 or c*x^2, while e + x (d + x (c + x (b + a x))) avoid this problem and needs less multiplications (on the most CPU's more expansive than an addition). Regards Jens "AES" <siegman at stanford.edu> schrieb im Newsbeitrag news:dckb96$o4j$1 at smc.vnet.net... |A Mathematic calculation is yielding a result of the form | | (x^4 + a (x^3 + a (x^2 + a ( x + a )))) | | for the case n = 4, and analogous results for larger n; and Mathematica | seems to be able to do some interesting simplifications and factoring of | these results. | | I'm sure I learned about this form in a math class somewhere along the | line, but this was 50+ years ago. Could some kind soul remind me of | what this form is called, and maybe some of its interesting properties? | | Thanks . . . |