A new arithmetic for scientific computation
Proc. of the symposium on A new approach to scientific computation
Solving algebraic problems with high accuracy
Proc. of the symposium on A new approach to scientific computation
Differentiation and generation of taylor coefficients in PASCAL-SC
Proc. of the symposium on A new approach to scientific computation
Differentiation in PASCAL-SC: type GRADIENT
ACM Transactions on Mathematical Software (TOMS)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Automatic Differentiation of Computer Programs
ACM Transactions on Mathematical Software (TOMS)
Computer Arithmetic in Theory and Practice
Computer Arithmetic in Theory and Practice
Automatic differentiation in prose
ACM SIGNUM Newsletter
Optimal Algorithms for Well-Conditioned Nonlinear Systems of Equations
IEEE Transactions on Computers
A second order geometric method for ray/parametric surface intersection
Computer Aided Geometric Design
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Cubicaliy convergent iterative methods for the solution of nonlinear systems of the multivariate Halley method, require first and second partial derivatives of the of the functions comprising the system. Automatic differentiation is used to automate the Halley method, HESSIAN and routines for the required operators and functions. A Pascal-SC which implements this method in a single-step iteration mode. The program nonlinear systems, and the results are compared with Newton's method.