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Hessian matrix

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  • Hessian matrix — In mathematics, the Hessian matrix (or simply the Hessian) is the square matrix of second order partial derivatives of a function; that is, it describes the local curvature of a function of many variables. The Hessian matrix was developed in the… …   Wikipedia

  • Hessian Affine region detector — The Hessian Affine region detector is a feature detector used in the fields of computer vision and image analysis. Like other feature detectors, the Hessian Affine detector is typically used as a preprocessing step to algorithms that rely on… …   Wikipedia

  • Matrix (mathematics) — Specific elements of a matrix are often denoted by a variable with two subscripts. For instance, a2,1 represents the element at the second row and first column of a matrix A. In mathematics, a matrix (plural matrices, or less commonly matrixes)… …   Wikipedia

  • Hessian — The term Hessian refers to the inhabitants of the German state of Hesse.Hessian may also mean: * Hessian (soldiers), soldiers from German states with in the Holy Roman Empire who fought in the American Revolutionary War and other conflicts *… …   Wikipedia

  • Matrix calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

  • Covariance matrix — A bivariate Gaussian probability density function centered at (0,0), with covariance matrix [ 1.00, .50 ; .50, 1.00 ] …   Wikipedia

  • Z-matrix (chemistry) — In chemistry, the Z matrix is a way to represent a system built of atoms. A Z matrix is also known as an internal coordinate representation. It provides a description of each atom in a molecule in terms of its atomic number, bond length, bond… …   Wikipedia

  • Symmetric matrix — In linear algebra, a symmetric matrix is a square matrix, A , that is equal to its transpose:A = A^{T}. ,!The entries of a symmetric matrix are symmetric with respect to the main diagonal (top left to bottom right). So if the entries are written… …   Wikipedia

  • Newton's method in optimization — A comparison of gradient descent (green) and Newton s method (red) for minimizing a function (with small step sizes). Newton s method uses curvature information to take a more direct route. In mathematics, Newton s method is an iterative method… …   Wikipedia

  • Mathematical optimization — For other uses, see Optimization (disambiguation). The maximum of a paraboloid (red dot) In mathematics, computational science, or management science, mathematical optimization (alternatively, optimization or mathematical programming) refers to… …   Wikipedia

  • Gauss–Newton algorithm — The Gauss–Newton algorithm is a method used to solve non linear least squares problems. It can be seen as a modification of Newton s method for finding a minimum of a function. Unlike Newton s method, the Gauss–Newton algorithm can only be used… …   Wikipedia

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