Systems of nonlinear equations

Overview One unknown Bracketing methods Newton's method: 1 unknown One unknown, polynomial zeros arbitrary real polynomials: find real zeroes Maehly's trick for polynomials zeroes of complex polynomials: Jenkins-Traub zeroes of complex polynomials: Hirano zeroes of complex polynomials: Laguerre all zeroes of a real polynomial: Bairstow Knuth's optimal evaluation scheme Systems of equations Newton's method: 2 unknowns Newton's method: n unknowns Gauss-Newton method ("nonlinear least squares") Levenberg-Marquardt method (m=n: nonlinear equations) orthogonal regression: "fitting an ellipse" orthogonal regression: "fitting a plane ellipse to data in 3D" orthogonal regression: explicit model SOR-Newton method n=2, graphically SOR-Newton method general n Newton-GMRES method general n more reading Systems of nonlinear equations back to the main menu