Solving nonlinear systems of equations with only one nonlinear variable
A method for solving systems of \(N+1\) equations in \(N+1\) unknowns \(y\in R\) and \(z\in R^ N\) of the form \(A(y)z+b(y)=0,\) where the \((N+1)\times N\) matrix A(y) and the vector b(y) are functions of y alone is presented. The problem is reduced to one equation in y only which is solved by Newton's method. Numerical experiments and two generalizations are discussed.
scientific article; zbMATH DE number 4153787
scientific article