Numerical calculation of eigenvalues and eigenvectors in MATLAB

With a single output argument, eig returns a vector of eigenvalues, 

With two output arguments, eig returns first a matrix W whose column vectors are the eigenvectors of A, and a diagonal matrix D, such that AW= WD, 

Computing extremal eigenvalues and their eigenvectors with eigs 

we need not compute all eigenvalues, but rather only certain ones, e g. the largest or smallest in magnitude. In M ATLAB this is done by eigs using the iterative methods discnssed below. We demonstrate the routine for a positive-definite matrix A, such as is obtained by discretizing a diffusion equation in one dimension. As eigs is compatible with sparse-format matrices we use this option, 

With a single output, eigs(A,k) returns the A eigenvalues of with the largest magnitude. eigs(A) performs this calculation for k=6. 

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