% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/HigherOrderPower.R
\name{HigherOrderPower}
\alias{HigherOrderPower}
\title{Higher-order Power Method for Symmetric Tensor Decomposition}
\usage{
HigherOrderPower(
  x,
  R = 1L,
  max_iter = 1000L,
  tol = 1e-08,
  init = c("random", "svd")
)
}
\arguments{
\item{x}{A symmetric rTensor Tensor object (all modes must be equal)}

\item{R}{Number of rank-1 components to extract (default: 1)}

\item{max_iter}{Maximum iterations per component (default: 1000)}

\item{tol}{Convergence tolerance (default: 1e-8)}

\item{init}{Initialization method: \code{"random"} (default) or \code{"svd"}}
}
\value{
A list with components:
  \describe{
    \item{lambdas}{Numeric vector of length R with eigenvalues}
    \item{vectors}{Matrix (n x R) where each column is a unit eigenvector}
    \item{residual}{Residual tensor after deflation}
    \item{converged}{Logical vector of length R}
    \item{iters}{Integer vector of iterations per component}
  }
}
\description{
Decomposes a symmetric tensor into a sum of rank-1 symmetric terms
using the higher-order power method (S-HOPM) with deflation.
}
\details{
For a d-th order symmetric tensor \eqn{T \in R^{n \times n \times \cdots \times n}},
finds \eqn{T \approx \sum_{r=1}^{R} \lambda_r v_r \otimes v_r \otimes \cdots \otimes v_r}.
}
\examples{
library(rTensor)
# Create a symmetric 3-mode tensor
n <- 5
v1 <- rnorm(n); v1 <- v1 / sqrt(sum(v1^2))
# T = 3.0 * v1 o v1 o v1
arr <- 3.0 * outer(outer(v1, v1), v1)
tnsr <- as.tensor(arr)
result <- HigherOrderPower(tnsr, R = 1)
result$lambdas  # should be close to 3.0
}
\references{
Kolda, T. G., & Mayo, J. R. (2011).
Shifted Power Method for Computing Tensor Eigenpairs.
SIAM Journal on Matrix Analysis and Applications.

De Lathauwer, L., De Moor, B., & Vandewalle, J. (2000).
On the Best Rank-1 and Rank-(R1, R2, ..., RN) Approximation of
Higher-Order Tensors. SIAM Journal on Matrix Analysis and Applications.
}
