First presenter Co-presenter(s)
Name :  Hiroshi Murakami * Name:   
E-mail: E-mail:  
Affiliation: Tokyo Metropolitan University Name:   
Department: Department of Mathematics and Information Sciences  E-mail:    
City: Tokyo Name:   
State/Province:   E-mail:    
Country: Japan Name:   
09-07  E-mail:    
Session: 9- Symbolic and Numeric Computation Schedule:
Saturday, 9:30
Related website:  
Title of
Solution of Approximated Roots of Equation by the Orthogonal Polynomial Expansion

When the roots are searched in the interval, the algebraic equation is expanded by the orthogonal polynomials associated with the interval. The roots are solved in the neighbor of the interval as the eigenvalues of the generalized companion matrix which corresponds to the orthogonal expansion. Similarly, the smooth non-linear equation is approximated by the truncated orthogonal expansion in the interval, and the approximated roots of the non-linear equation in the interval are solved by the above generalized companion method as the roots of the expansion. The condition of the set of orthogonal polynomials in the interval is much better than that of monomials (x-c)^k (which is also the basis for Taylor expansion). Therefore, the calculated approximated roots are expected to give smaller residuals with the restricted precision of the floating point numbers. Some examples would be shown which solved equations approximately by the applications of the orthogonal polynomial expansion.