In general computing the Cholesky factorization of a symmetric matrix A is the fastest method to check if A is positive definite.
For banded matrices there is a specialized algorithm of computing the Cholesky factorization, which is faster than the Cholesky factorization of a sparse matrix. Such algorithm is not available in Matlab.
Symmetric positive definite matrices have positive elements on the main diagonal.
You may also apply the Gershgorin circle theorem to find constraints on eigenvalues of A. If this theorem shows that all eigenvalues are positive, then it proves, that the matrix A is positive definite.
The last two methods are very fast and can be used as fast checks, but do not work in general.