Time reversal and Lanczos iterations

Lanczos iterated time-reversal.

A new iterative time-reversal algorithm capable of identifying and focusing on multiple scatterers in a relatively small number of iterations is developed. It is recognized that the traditional iterated time-reversal method is based on utilizing power iterations to determine the dominant eigenpairs of the time-reversal operator. The convergence properties of these iterations are known to be sub...

Polynomial filtered Lanczos iterations with applications in Density Functional Theory

The most expensive part of all Electronic Structure Calculations based on Density Functional Theory, lies in the computation of an invariant subspace associated with some of the smallest eigenvalues of a discretized Hamiltonian operator. The dimension of this subspace typically depends on the total number of valence electrons in the system, and can easily reach hundreds or even thousands when l...

Computation of Large Invariant Subspaces Using Polynomial Filtered Lanczos Iterations with Applications in Density Functional Theory

The most expensive part of all electronic structure calculations based on density functional theory lies in the computation of an invariant subspace associated with some of the smallest eigenvalues of a discretized Hamiltonian operator. The dimension of this subspace typically depends on the total number of valence electrons in the system, and can easily reach hundreds or even thousands when la...

Accelerating Iterations Involving Eigenvalue or Singular Value Decomposition by Block Lanczos with Warm Start

Many machine learning problems are solved by algorithms that involve eigenvalue decomposition (EVD) or singular value decomposition (SVD) in each iteration. Therefore, these algorithms suffer from the high computation cost of multiple EVD/SVDs. To relieve this issue, we introduce the block Lanczos method to replace the original exact EVD/SVD in each iteration by solving it approximately, yet st...

Time - Reversal And