solving multiple nonlinear algebraic equations indicating that is the rate for newton' method similar computation using the secant methodgives the rates secant here it seems that : is the limit remark if we in the bisection method think of the length of the current interval containing the solution as the error en then ( works perfectly since enc and but if en is the true error jx xn jit is easily seen from sketch that this error can oscillate between the current interval length and potentially very small value as we approach the exact solution the corresponding rates qn fluctuate widely and are of no interest solving multiple nonlinear algebraic equations so far in this we have considered single nonlinear algebraic equation howeversystems of such equations arise in number of applicationsforemost nonlinear ordinary and partial differential equations of the previous algorithmsonly newton' method is suitable for extension to systems of nonlinear equations abstract notation suppose we have nonlinear equationswritten in the following abstract formf xn xn :::dfn xn ( ( ( ( ( it will be convenient to introduce vector notation / xn the system can now be written as xd as specific example on the notation abovethe system cos xyx dx ( (