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QR Decomposition

Given a matrix A, its QR-decomposition is a matrix decomposition of the form

A=QR,

where R is an upper triangular matrix and Q is an orthogonal matrix, i.e., one satisfying

Q^(T)Q=I,

where Q^(T) is the transpose of Q and I is the identity matrix. This matrix decomposition can be used to solve linear systems of equations.

QR decomposition is implemented in the Wolfram Language as QRDecomposition[m].

See also

Cholesky Decomposition, LU Decomposition, Matrix Decomposition, PSLQ Algorithm, Singular Value Decomposition

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References

Gentle, J. E. "QR Factorization." §3.2.2 in Numerical Linear Algebra for Applications in Statistics. Berlin:Springer-Verlag, pp. 95-97, 1998.Householder, A. S. The Numerical Treatment of a Single Non-Linear Equations. New York: McGraw-Hill, 1970.Nash, J. C. Compact Numerical Methods for Computers: Linear Algebra and Function Minimisation, 2nd ed. Bristol, England: Adam Hilger, pp. 26-28, 1990.Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "QR Decomposition." §2.10 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 91-95, 1992.Stewart, G. W. "A Parallel Implementation of the QR Algorithm." Parallel Comput. 5, 187-196, 1987. ftp://thales.cs.umd.edu/pub/reports/piqra.ps.

Cite this as:

Weisstein, Eric W. "QR Decomposition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/QRDecomposition.html

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