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A Jacobian Matrix is defined as :

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If we have discrete data and we are applying any numerical modelling approach how will end elements of the matrix be calculated. for example : if central difference is applied then df(i)=df(i+1)-df(i-1) .based on this df(1) cannot be calculated.

shrey
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  • the subsripts refer to the different dimensions of the problem space; your question as asked seems to be interpreting them as n values of a single variable. For the Jacobian to make sense there must be an n-dimensional space, and the n functions are the transformations of one set of n descriptive variables to a new set. Each variable should have available multiple values near the multidimensional point for which the Jacobian is to be evaluated. – Peter Diehr Mar 05 '16 at 12:46
  • my doubt is that suppose we use central difference scheme then it is possible to compute elements in first row or last row since there are no elements before(or after) – shrey Mar 05 '16 at 15:56

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