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Householder's method applied to the real-valued function f(x) is the same as applying Newton's method + = ′ to find the zeros of the function: = | (/) | /. In particular, d = 1 gives Newton's method unmodified and d = 2 gives Halley's method.
In linear algebra, a Householder transformation (also known as a Householder reflection or elementary reflector) is a linear transformation that describes a reflection about a plane or hyperplane containing the origin. The Householder transformation was used in a 1958 paper by Alston Scott Householder. [1]
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.
Newton's method is also important because it readily generalizes to higher-dimensional problems. Householder's methods are a class of Newton-like methods with higher orders of convergence. The first one after Newton's method is Halley's method with cubic order of convergence.
Alston Scott Householder (5 May 1904 – 4 July 1993) was an American mathematician who specialized in mathematical biology and numerical analysis. He is the inventor of the Householder transformation and of Householder's method .
The Householder scandal has been exposed and prosecuted, but it's still being exploited by politicians and activists to erode fundamental rights. Opinion: Householder scandal no excuse for ...
A court docket entry on Tuesday showed that the court granted Boyd Householder’s request to remove the GPS monitor but denied the same request from Stephanie Householder. The Householders opened ...
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