Jump to content
  • Advertisement
Sign in to follow this  

Generalized Least Square Method

This topic is 3735 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic.

If you intended to correct an error in the post then please contact us.

Recommended Posts

Generalized Least Square Method(Least Cubic Method ) When studying the relating relations between the two variable numbers (x, y), we can get a series of binate data(x1, y1, x2, y2.....xm, ym), describing the data into the x - y orthogonal coordinate system(Chart), the points are found near a curve. suppose the one-variant non-linear variant of the curve such as (Formula 1) http://www.eaihua.com/images/eZxsc.GIF y = a0 + a1 xi ^k (1) There into, a0, a1 and k are arbitrary real numbers To set the curve variant, the numbers of a0, a1 and k must be set. Use the same way with “The Least Square Method data regression” based on the square sum of the deviation of the true measure value yi and computing value. Order: φ = ∑(yi - y)^2 (2) Take (Formula 1) to (Formula 2) to get : φ = ∑(yi - a0 - a1 xik )^2 (3) When the square of ∑(yi - a0 - a1 xik ) is the smallest, we can use functionφ to get the partial differential coefficients of a0, a1 and k, make the three partial differential coefficients zero. http://www.eaihua.com/images/3a1.GIF (4) http://www.eaihua.com/images/3a2.GIF (5) http://www.eaihua.com/images/3a3.GIF (6) Get three variant groups about a0,a1 and k which are the unknown numbers, solve the groups can get mathematical model. Also, we can judge the right of the mathematical model with the help of correlation coefficient R, statistical variable F, residual standard deviation S to judge, it is better that R tends to 1,the absolute value of F is bigger and S tends to 0. the validation is good, but error of model computing sometimes are big, to improve the mathematical model farther, the biggest error, equal error and the equal relating error of computing model are computed to validate the model. The Method to do multivariate nonlinear model chart http://www.eaihua.com/images/sw1.GIF http://www.eaihua.com/images/sw2.GIF Web address: http://www.eaihua.com

Share this post

Link to post
Share on other sites
Sign in to follow this  

  • Advertisement

Important Information

By using GameDev.net, you agree to our community Guidelines, Terms of Use, and Privacy Policy.

We are the game development community.

Whether you are an indie, hobbyist, AAA developer, or just trying to learn, GameDev.net is the place for you to learn, share, and connect with the games industry. Learn more About Us or sign up!

Sign me up!