Computes approximated a pair of eigenvalue and eigenvector.
mu = linalg_rayleighiteration ( A , mu0 , b0 ) mu = linalg_rayleighiteration ( A , mu0 , b0 , rtol ) mu = linalg_rayleighiteration ( A , mu0 , b0 , rtol , itmax ) mu = linalg_rayleighiteration ( A , mu0 , b0 , rtol , itmax , verbose ) [mu,b] = linalg_rayleighiteration ( ... ) [mu,b,iter] = linalg_rayleighiteration ( ... )
a n-by-n matrix of doubles, real, symetric
a 1-by-1 matrix of doubles, an estimated eigenvalue
a n-by-1 matrix of doubles, an estimated eigenvector
a 1-by-1 matrix of doubles (default rtol = %eps), a relative tolerance
a 1-by-1 matrix of doubles, integer value (default itmax = 100), a maximum number of iterations
a 1-by-1 matrix of booleans (default verbose = %f), set to true to print convergence messages
a 1-by-1 matrix of doubles, an approximated eigenvalue
a n-by-1 matrix of doubles, an approximated eigenvector
the number of iterations performed
Uses Rayleigh iterations to find an approximate eigenvalue and an approximate eigenvector.
The algorithm stops if norm(A*b-mu*b) < rtol*norm(mu*b).