Assuming there is a square matrix A and vector b about to be multiplied.
[A]{b}={c}
However I am interested only in the maximum value within the resulted vector c. Is there a way to find that without performing normal matrix multiplication and then search in the results?
Does the matrix A have any other properties besides it being a square matrix? real, symmetric, positive definite, sparse, etc.
FWIW, the largest eigenvalue and eigenvector can be calculated using the Power algorithm. This might provide some useful information.
Power Iteration