Givens Rotation
Givens Rotations and QR decomposition
givens(A)
A |
numeric square matrix. |
givens(A) returns a QR decomposition (or factorization) of the
square matrix A by applying unitary 2-by-2 matrices U such
that U * [xk;xl] = [x,0] where x=sqrt(xk^2+xl^2)
List with two matrices Q and R, Q orthonormal and
R upper triangular, such that A=Q%*%R.
Golub, G. H., and Ch. F. van Loan (1996). Matrix Computations. Third edition, John Hopkins University Press, Baltimore.
## QR decomposition A <- matrix(c(0,-4,2, 6,-3,-2, 8,1,-1), 3, 3, byrow=TRUE) gv <- givens(A) (Q <- gv$Q); (R <- gv$R) zapsmall(Q %*% R) givens(magic(5))
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