in this paper, we obtain two intrinsic integral inequalities of hessian manifolds.

We analyse the matrix momentum algorithm, which provides an efficient approximation to on-line Newton’s method, by extending a recent statistical mechanics framework to include second order algorithms. We study the efficacy of this method when the Hessian is available and also consider a practical implementation which uses a single example estimate of the Hessian. The method is shown to provide...

Let us consider a truncated matroid MΓr of rank r graphic graph Γ. The basis for is the set forests with edges in We this generating function and compute its Hessian. In paper, we show that Hessian complete or bipartite does not vanish by calculating eigenvalues matrix. Moreover, matrix has exactly one positive eigenvalue. As an application, strong Lefschetz property Artinian Gorenstein algebra...

In this paper, we solve unconstrained optimization problem using a free line search steepest descent method. First, we propose a double parameter scaled quasi Newton formula for calculating an approximation of the Hessian matrix. The approximation obtained from this formula is a positive definite matrix that is satisfied in the standard secant relation. We also show that the largest eigen value...

The output weight optimization-hidden weight optimization (OWO-HWO) algorithm for training the multilayer perceptron alternately updates the output weights and the hidden weights. This layer-by-layer training strategy greatly improves convergence speed. However, in HWO, the desired net function actually evolves in the gradient direction, which inevitably reduces efficiency. In this paper, two i...

We propose a method for computation of the Hessian of axially symmetric functions on the roto-translation group SE(3). Eigendecomposition of the resulting Hessian is then used for curvature estimation of tubular structures, similar to how the Hessian matrix of 2D or 3D image data can be used for orientation estimation. This paper focuses on a new implementation of a Gaussian regularized Hessian...

Abst ract. This pap er pr esents th e applica tion of signal flow gra phs to the det ermination of the exact values of gradient vecto r and hessian matrix for a linear system. It is shown all information about the gradient and hessian is cont ained in the or iginal and adjoint signa l flow graphs at different terminations. To det ermine the gra dient we have to perform two analyses , and t o ge...