Newtons method in two variables

Let be chosen. We need to generate tire sequence of vectors (x y ) recursively as follows  

Under suitable condibons, the sequence x ,yj will converge to a vector (u,v) that satisfies 

Newton s method is most likely to work when the initial vector (x ,y ) is close to a solution. It is not necessary that the system has only one solution. 

Values of above-mentioned two equations can be calculated using x = 1.900677 and y = 0.311219 from Table 1.7 as 

Process engineering and design using Visual Basic 

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