Search results
Results from the WOW.Com Content Network
Carl Friedrich Gauss in 1810 devised a notation for symmetric elimination that was adopted in the 19th century by professional hand computers to solve the normal equations of least-squares problems. [7] The algorithm that is taught in high school was named for Gauss only in the 1950s as a result of confusion over the history of the subject. [8]
Shoelace scheme for determining the area of a polygon with point coordinates (,),..., (,). The shoelace formula, also known as Gauss's area formula and the surveyor's formula, [1] is a mathematical algorithm to determine the area of a simple polygon whose vertices are described by their Cartesian coordinates in the plane. [2]
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 .
The textbook Numerical Mathematics by Alfio Quarteroni, Sacco and Saleri, lists a modified version of the algorithm which avoids some of the divisions (using instead multiplications), which is beneficial on some computer architectures. Parallel tridiagonal solvers have been published for many vector and parallel architectures, including GPUs [7 ...
In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: + (). In this case
Gauss–Kronrod rules are extensions of Gauss quadrature rules generated by adding n + 1 points to an n-point rule in such a way that the resulting rule is of order 2n + 1. This allows for computing higher-order estimates while re-using the function values of a lower-order estimate.
Gauss–Kronrod formulas are extensions of the Gauss quadrature formulas generated by adding + points to an -point rule in such a way that the resulting rule is exact for polynomials of degree less than or equal to + (Laurie (1997, p. 1133); the corresponding Gauss rule is of order ).
Gauss–Legendre methods are implicit Runge–Kutta methods. More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on s points has order 2s. [1] All Gauss–Legendre methods are A-stable. [2] The Gauss–Legendre method of order two is the implicit midpoint rule.