Compute the singular-value decomposition of a matrix Eigen. Both methods are iterative.
The result consists of two orthonormal matrices,
SVD(X, method = c("Jacobi", "eigen"), tol = sqrt(.Machine$double.eps),
max.iter = 100)a square symmetric matrix
either "Jacobi" (the default) or "eigen"
zero and convergence tolerance
maximum number of iterations
a list of three elements: d-- singular values, U-- left singular vectors, V-- right singular vectors
The default method is more numerically stable, but the eigenstructure method is much simpler. Singular values of zero are not retained in the solution.
svd, the standard svd function
# NOT RUN {
C <- matrix(c(1,2,3,2,5,6,3,6,10), 3, 3) # nonsingular, symmetric
C
SVD(C)
# least squares by the SVD
data("workers")
X <- cbind(1, as.matrix(workers[, c("Experience", "Skill")]))
head(X)
y <- workers$Income
head(y)
(svd <- SVD(X))
VdU <- svd$V %*% diag(1/svd$d) %*%t(svd$U)
(b <- VdU %*% y)
coef(lm(Income ~ Experience + Skill, data=workers))
# }
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