LSE Solution

Systems of linear equations via QR decomposition.

qrSolve(A, b)

Arguments

A

numerical matrix with nrow(A)>=ncol(A).

b

numerical vector with length(b) == nrow(A).

Details

Solves (overdetermined) systems of linear equations via QR decomposition.

Value

The solution of the system as vector.

References

Trefethen, L. N., and D. Bau III. (1997). Numerical Linear Algebra. SIAM, Society for Industrial and Applied Mathematics, Philadelphia.

See also

householder

Examples

A <- matrix(c(0,-4,2, 6,-3,-2, 8,1,-1), 3, 3, byrow=TRUE)
b <- c(-2, -6, 7)
qrSolve(A, b)
#> [1] 1 2 3

##  Solve an overdetermined linear system of equations
A <- matrix(c(1:8,7,4,2,3,4,2,2), ncol=3, byrow=TRUE)
b <- rep(6, 5)
x <- qrSolve(A, b)
qr.solve(A, rep(6, 5)); x
#> [1]  1.074236 -2.331878  2.436681
#> [1]  1.074236 -2.331878  2.436681