Quasi- Newton Methods for Nonlinear Equations
Journal of the ACM (JACM)
A Procedure for Detecting Intersections of Three-Dimensional Objects
Journal of the ACM (JACM)
Note on "Solution of Nonlinear Equations"
IEEE Transactions on Computers
Optimal operation of blast furnace stoves
Automatica (Journal of IFAC)
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The need to solve a set of n simultaneous nonlinear equations in n unknowns arises in many areas of science and engineering. The equations can be expressed in the form: [equation] [equation] [equation] It will be assumed that at least one real solution exists and that the functions are continuous and possess continuous first derivatives. These assumptions are often good ones in dealing with equations arising in many physical systems. However, the functions themselves are often long, complex and expensive (in terms of computer time) to evaluate and the value of their derivatives can only be inferred from a finite difference approximation. Therefore, solution methods which keep the number of functional evaluations (i.e. the number of times the f vector needs to be evaluated) to a minimum become very attractive.