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In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel .
Linear programming problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is a linear combination of n variables. There are m constraints, each of which places an upper bound on a linear combination of the n variables. The goal is to maximize the value ...
A substitution σ is called a linear substitution if tσ is a linear term for some (and hence every) linear term t containing precisely the variables of σ ' s domain, i.e. with vars(t) = dom(σ). A substitution σ is called a flat substitution if xσ is a variable for every variable x.
Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point.
In operations research, the Big M method is a method of solving linear programming problems using the simplex algorithm.The Big M method extends the simplex algorithm to problems that contain "greater-than" constraints.
A linear Volterra equation of the first kind can always be reduced to a linear Volterra equation of the second kind, assuming that (,).Taking the derivative of the first kind Volterra equation gives us: = + (,) Dividing through by (,) yields: = (,) (,) Defining ~ = (,) and ~ (,) = (,) completes the transformation of the first kind equation into a linear Volterra equation of the second kind.
The envelope E 1 is the limit of intersections of nearby curves C t.; The envelope E 2 is a curve tangent to all of the C t.; The envelope E 3 is the boundary of the region filled by the curves C t.
A multilinear map of one variable is a linear map, and of two variables is a bilinear map. More generally, for any nonnegative integer , a multilinear map of k variables is called a k-linear map. If the codomain of a multilinear map is the field of scalars, it is called a multilinear form.