Concepts inSoftware for estimating sparse Hessian matrices
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 19th century by the German mathematician Ludwig Otto Hesse and later named after him. Hesse himself had used the term "functional determinants".
more from Wikipedia
Matrix (mathematics)
In mathematics, a matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements is Matrices of the same size can be added or subtracted element by element. The rule for matrix multiplication is more complicated, and two matrices can be multiplied only when the number of columns in the first equals the number of rows in the second.
more from Wikipedia
Sparse matrix
In the subfield of numerical analysis, a sparse matrix is a matrix populated primarily with zeros. The term itself was coined by Harry M. Markowitz. Conceptually, sparsity corresponds to systems which are loosely coupled. Consider a line of balls connected by springs from one to the next; this is a sparse system. By contrast, if the same line of balls had springs connecting each ball to all other balls, the system would be represented by a dense matrix.
more from Wikipedia
Nonlinear programming
In mathematics, nonlinear programming (NLP) is the process of solving a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.
more from Wikipedia
Gradient
In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is that rate of increase. A generalization of the gradient for functions on a Euclidean space that have values in another Euclidean space is the Jacobian. A further generalization for a function from one Banach space to another is the Fréchet derivative.
more from Wikipedia
Subroutine
In computer science, a subroutine, also termed procedure, function, routine, method, or subprogram, is a part of source code within a larger computer program that performs a specific task and is relatively independent of the remaining code. As the name subprogram suggests, a subroutine behaves in much the same way as a computer program that is used as one step in a larger program or another subprogram.
more from Wikipedia
Function (mathematics)
In mathematics, a function is a relation between a set of inputs and a set of potential outputs with the property that each input is related to exactly one output. An example of such a relation is defined by the rule f(x) = x, which relates an input x to its square, which are both real numbers. The output of the function f corresponding to an input x is denoted by f(x) (read "f of x"). If the input is ¿3, then the output is 9, and we may write f(¿3) = 9.
more from Wikipedia