Abstract
An extension of Gauss' least-squares theory as applied to the situation of nonorthogonal polynomials has led to the development of an efficient algorithm for computing the coefficients of polynomial surfaces. The extension is based on the powerful, dimensionally invariant concept of the High Speed Matrix Generator (HSMG) which computes and stores only the minimum number of nonrepeating terms needed to form the coefficient matrix. Because the 2-dimensional HSMG matrix for a given order polynomial contains the necessary terms for all lower order fits, lower order surface approximations are evaluated easily in only a fraction of the time that is required to form the independent terms of the coefficient matrix. The number of operations for a given order ( N) of fit has been reduced from N 4 to N 2, resulting in a substantial reduction in computer execution time. A comparison was made between the algorithm described here and the well-known algorithm of J. C. Davis. From a 50 × 50 grid (2500 data points), computing the coefficients for degrees 1–10 took 2.84 min with our program and 1.4 h with the Davis program on an IBM AT microcomputer. This represents an efficiency increase of about a factor of 30, or equivalently, almost 3000%.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
