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- Hessian_matrix abstract "In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants". Given the real-valued functionif all second partial derivatives of f exist and are continuous over the domain of the function, then the Hessian matrix of f iswhere x = (x1, x2, ..., xn) and Di is the differentiation operator with respect to the ith argument. ThusBecause f is often clear from context, is frequently abbreviated to .The Hessian matrix is related to the Jacobian matrix by = .The determinant of the above matrix is also sometimes referred to as the Hessian.Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function. That is, where J is the Jacobian matrix, which is a vector (the gradient) for scalar-valued functions. The full Hessian matrix can be difficult to compute in practice; in such situations, quasi-Newton algorithms have been developed that use approximations to the Hessian. The best-known quasi-Newton algorithm is the BFGS algorithm.[citation needed]".
- Hessian_matrix wikiPageID "412108".
- Hessian_matrix wikiPageRevisionID "595152302".
- Hessian_matrix hasPhotoCollection Hessian_matrix.
- Hessian_matrix subject Category:Differential_operators.
- Hessian_matrix subject Category:Matrices.
- Hessian_matrix subject Category:Morse_theory.
- Hessian_matrix subject Category:Multivariable_calculus.
- Hessian_matrix type Abstraction100002137.
- Hessian_matrix type Arrangement107938773.
- Hessian_matrix type Array107939382.
- Hessian_matrix type DifferentialOperators.
- Hessian_matrix type Function113783816.
- Hessian_matrix type Group100031264.
- Hessian_matrix type MathematicalRelation113783581.
- Hessian_matrix type Matrices.
- Hessian_matrix type Matrix108267640.
- Hessian_matrix type Operator113786413.
- Hessian_matrix type Relation100031921.
- Hessian_matrix comment "In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a function. It describes the local curvature of a function of many variables. The Hessian matrix was developed in the 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse originally used the term "functional determinants".".
- Hessian_matrix label "Hesse-Matrix".
- Hessian_matrix label "Hessiaan".
- Hessian_matrix label "Hessian matrix".
- Hessian_matrix label "Hessiano".
- Hessian_matrix label "Macierz Hessego".
- Hessian_matrix label "Matrice hessiana".
- Hessian_matrix label "Matrice hessienne".
- Hessian_matrix label "Matriz hessiana".
- Hessian_matrix label "Гессиан функции".
- Hessian_matrix label "ヘッセ行列".
- Hessian_matrix label "海森矩阵".
- Hessian_matrix sameAs Hessova_matice.
- Hessian_matrix sameAs Hesse-Matrix.
- Hessian_matrix sameAs Matriz_hessiana.
- Hessian_matrix sameAs Matrice_hessienne.
- Hessian_matrix sameAs Matrice_hessiana.
- Hessian_matrix sameAs ヘッセ行列.
- Hessian_matrix sameAs 헤세_행렬.
- Hessian_matrix sameAs Hessiaan.
- Hessian_matrix sameAs Macierz_Hessego.
- Hessian_matrix sameAs Hessiano.
- Hessian_matrix sameAs m.0256s2.
- Hessian_matrix sameAs Q620495.
- Hessian_matrix sameAs Q620495.
- Hessian_matrix sameAs Hessian_matrix.
- Hessian_matrix wasDerivedFrom Hessian_matrix?oldid=595152302.
- Hessian_matrix isPrimaryTopicOf Hessian_matrix.