First presenter Co-presenter(s)
Name :  B. Palancz Name:  P. Zaletnyik
E-mail: E-mail:  
Affiliation: Budapest University of Technology and Economy Name:  J. Awange
Department: Department of Photogrammetry and Geoinformatics  E-mail:    
City: Name:  R. H. *Lewis *
State/Province:   E-mail:    
Country: Hungary,
and USA
04-05  E-mail:    
Session: 4- Elimination Theory and Applications Schedule:
Sunday, 9:30
Related website:  
Title of
Application of Symbolic - Numeric Algebra in Geodesy

Most often geodetic problems are represented as system of multivariable polynomials. The bottleneck in solving such systems is finding out proper initial values for local iterative numerical methods. If the problem is relatively modest in size, computer algebraic methods like Groebner basis or Dixon resultant can give symbolic solution. To extend this result for overdetermined system one may use Gauss-Jacobi combinatoric solution employing the symbolic result many times. However, when the number of the combinatoric subsystems is very high, it is reasonable to employ global, robust numerical method like linear homotopy. In order to avoid the computation of all possible paths, consequently to simplify homotopy solution, the initial value of the start system can be evaluated from the symbolic solution of a subsystem. To illustrate this strategy a real world geodetic problem is presented. The 3 point problem of the 3D affine transformation is solved with Dixon resultant computed with EDF method. Then employing this result as initial value of the start system of linear homotopy as numerical method, the solution is computed for N = 1138 points as well.