The Theory of Matrices in Numerical Analysis (Dover Books on Mathematics) by Alston S. Householder, 2006-01-20
Principles of Numerical Analysis by Alston S. Householder, 2006-09-29
Bibliography on numerical analysis by Alston Scott Householder, 1955-01-01
Numerical Treatment of a Single Nonlinear Equation (Pure & Applied Mathematics) by
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The following article was written bygd G.W. Stewart, University of Maryland, and is reprinted with permission from SIAM News, Vol. 26, October 1993.
Alston Scott Householder (1904-1993)
On July 4, 1993, Alston Scott Householder, former president of SIAM, died of a massive stroke. He is survived by his wife, Heidi, his daughter, Jackie, and his son, John. Two weeks before his death he had attended the Householder Symposium at Lake Arrowhead, California, the 12th in a series of research of gatherings he had started in 1961 in Gatlinburg Tennessee. Alston was feeble but alert, and he enjoyed the opportunity to see old friends once again. He will be greatly missed.
Householder was born on May 5, 1904 in Rockford, Illinois, and shortly thereafter moved to Alabama, where he spent his childhood. He received two degrees in philosophy, a BA from Northwestern University in 1925 and an MA from Cornell University in 1927. Until 1937 he held various teaching positions in mathematics.
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Householder transformation
Concept in linear algebra
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]
Its analogue over general inner product spaces is the Householder operator.
Definition
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Transformation
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The reflection hyperplane can be defined by its normal vector, a unit vector (a vector with length ) that is orthogonal to the hyperplane. The reflection of a point about this hyperplane is the linear transformation:
where is given as a column unit vector with conjugate transpose, and considering as a vector from the origin to the point .
Householder matrix
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The matrix constructed from this transformation can be expressed in terms of an outer product as: