At each scale, interest points are those points that simultaneously are local extrema of both the determinant and trace of the Hessian matrix.
22.
The Hessian matrix plays an important role in Morse theory and catastrophe theory, because its kernel and eigenvalues allow classification of the critical points.
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The Hessian matrix of a convex function is critical point is a local maximum, local minimum, or a saddle point, as follows:
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Computing and storing the full Hessian matrix takes memory, which is infeasible for high-dimensional functions such as the loss functions of BFGS.
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Finding these principal curvatures amounts to solving for the eigenvalues of the second-order Hessian matrix, "'H " ':
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However, these quantities are technically defined by the true Hessian matrix, and the BFGS approximation may not converge to the true Hessian matrix.
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However, these quantities are technically defined by the true Hessian matrix, and the BFGS approximation may not converge to the true Hessian matrix.
28.
The covariance matrix C _ k adapts to the inverse of the Hessian matrix H, up to a scalar factor and small random fluctuations.
29.
But then the fonts are missing, and for the expanded-form example at Hessian matrix that makes everything but the fraction lines disappear.
30.
AutoChem symbolically differentiates the time derivatives to give the Jacobian matrix, and symbolically differentiates the Jacobian matrix to give the Hessian matrix and the adjoint.
