  It might be inadequate for the line search technique for Newton's method to
use only one floating point number. A column vector of the same size as the
gradient might be better than a mere float number to accelerate each of the
gradient elements with different rates. Moreover, a square matrix of the same
order as the Hessian matrix might be helpful to correct the Hessian matrix.
Chiang applied something between a column vector and a square matrix, namely a
diagonal matrix, to accelerate the gradient and further proposed a faster
gradient variant called quadratic gradient. In this paper, we present a new way
to build a new version of the quadratic gradient. This new quadratic gradient
doesn't satisfy the convergence conditions of the fixed Hessian Newton's
method. However, experimental results show that it sometimes has a better
performance than the original one in convergence rate. Also, Chiang speculates
that there might be a relation between the Hessian matrix and the learning rate
for the first-order gradient descent method. We prove that the floating number
$\frac{1}{\epsilon + \max \{| \lambda_i | \}}$ can be a good learning rate of
the gradient methods, where $\epsilon$ is a number to avoid division by zero
and $\lambda_i$ the eigenvalues of the Hessian matrix.
