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In mathematics, and more specifically in numerical analysis, Householder's methods are a class of root-finding algorithms that are used for functions of one real variable with continuous derivatives up to some order d + 1. Each of these methods is characterized by the number d, which is known as the order of the method.
Also, notice = = <, > = (since is by definition a unit vector), and so is an eigenvalue with multiplicity . The determinant of a Householder reflector is − 1 {\textstyle -1} , since the determinant of a matrix is the product of its eigenvalues, in this case one of which is − 1 {\textstyle -1} with the remainder being 1 {\textstyle 1} (as in ...
Householder's method: Scientific career: Fields: Numerical Analysis Linear Algebra [1] Institutions: Oak Ridge National Laboratory [2] Thesis: The Dependence of a Focal Point Upon Curvature in the Calculus of Variations (1937) Doctoral advisor: Gilbert Ames Bliss [3]
MathWorld covers something it calls Householder's method, but it's really a variation on Halley's method and doesn't support the material given here. A Google search turned up dozens of sources for "Householder's method" but every one of them seems to be referring to the Householder transformation which is a completely different subject. That ...
In linear algebra, the Householder operator is defined as follows. [1] Let be a finite-dimensional inner product space with inner product , and unit vector.Then : is defined by
This method has greater numerical stability than the Gram–Schmidt method above. The following table gives the number of operations in the k-th step of the QR-decomposition by the Householder transformation, assuming a square matrix with size n.
The Householders opened Circle of Hope near Humansville in 2006. They closed it shortly after about two dozen girls were removed amid an investigation in August 2020.
Householder may refer to: . Householder, a person who is the head of a household; Householder (Buddhism), a Buddhist term most broadly referring to any layperson Householder (surname), notable people with the surname