I Residual of an algebraic equation

I
Thread starter feynman1
Start date Mar 6, 2022

AI Thread Summary

To solve the equations f(x,y)=0 and g(x,y)=0, Newton iteration is employed, allowing for the definition of a residual at each iteration. The term 'residual of x' or 'residual of y' refers to the individual components of the overall residual from the iteration process. This suggests that the residual should be analyzed separately for each variable rather than as a collective measure of the equations. Understanding these residuals is crucial for assessing convergence in the iterative process. Clarifying these terms enhances the comprehension of the Newton iteration method in solving algebraic equations.

Mar 6, 2022

feynman1

To solve a set of equations f(x,y)=0, g(x,y)=0, where x, y, f, g are scalars, use Newton iteration. At each iteration step i, can certainly define the residual of this set of equations. But what's meant by the term 'residual of x' or 'residual of y'? Not the 'residual of the equations'?

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Mar 7, 2022

nuuskur

Science Advisor

My guess would be take the residual of the iteration and look at the components separately.

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