Newtons Method and Parallel Computations

When several processors are available and parallel computing can be exploited, it is possible to make Newton s method more high performance. 

However, the modified Newton methods still have two of the shortcomings of Newton s method when a single processor is available  

When the Jacobian has to be updated and the matrix is dense, the system must be called Wy times. 

The Jacobian must be factorized at each iteration to solve the linear system (7.38). 

Both of these operations can be fully parallelized. Thus, when np 1 processors are available, it is possible to reduce their computational time proportional to the number of processors. 

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