FoldUnfold Table of Contents Applying The Fixed Point Method for Solving Systems of Two Nonlinear Equations Example 1 Applying The Fixed Point Method for Solving Systems of Two Nonlinear Equations Be sure to review the following pages regarding The Fixed Point method for solving systems of two nonlinear equations: The Fixed Point Method for Solving Systems of Two … [Read more...]

## The Algorithm for The Fixed Point Method for Solving Systems of Two Nonlinear Equations

FoldUnfold Table of Contents The Algorithm for The Fixed Point Method for Solving Systems of Two Nonlinear Equations The Algorithm for The Fixed Point Method for Solving Systems of Two Nonlinear Equations We will now summarize The Fixed Point Method for Solving Systems of Two Nonlinear Equations in the following algorithm. Let $\left\{\begin{matrix} f(x, y) = 0\\ g(x, y) … [Read more...]

## Convergence of The Fixed Point Method for Solving Systems of Two Nonlinear Equations

FoldUnfold Table of Contents Convergence of The Fixed Point Method for Solving Systems of Two Nonlinear Equations Convergence of The Fixed Point Method for Solving Systems of Two Nonlinear Equations We will now develop criterion to ensure that the successive iterations converge to $(\alpha, \beta)$. If $(\alpha, \beta)$ is a solution to the system prescribed above, then … [Read more...]

## The Fixed Point Method for Solving Systems of Two Nonlinear Equations

FoldUnfold Table of Contents The Fixed Point Method for Solving Systems of Two Nonlinear Equations The Fixed Point Method for Solving Systems of Two Nonlinear Equations We will now look at an extension to The Fixed Point Method for Approximating Roots. Suppose that a solution $(\alpha, \beta)$ exists to the system of two nonlinear equations: (1) \begin{align} \quad … [Read more...]

## Newton’s Method for Solving Systems of Many Nonlinear Equations

FoldUnfold Table of Contents Newton's Method for Solving Systems of Many Nonlinear Equations Newton's Method for Solving Systems of Many Nonlinear Equations We will now extend Newton's Method further to systems of many nonlinear equations. Consider the general system of $n$ linear equations in $n$ unknowns: (1) \begin{align} f_1(x_1, x_2, …, x_n) = 0 \\ f_2(x_1, x_2, …, … [Read more...]