 Instead, it constructs an orthogonal basis of the invariant subspace by combining two main ingredients. The first is a filtering technique to dampen the undesirable contribution of the largest eigenvalues at each matrix-vector product in the Lanczos algorithm.

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This technique employs a well-selected low pass filter polynomial, obtained via a conjugate residual-type algorithm in polynomial space. The second ingredient is the Lanczos algorithm with partial reorthogonalization.

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Experiments are reported to illustrate the efficiency of the proposed scheme compared to state-of-the-art implicitly restarted techniques. Computation of large invariant subspaces using polynomial filtered lanczos iterations with applications in density functional theory. T1 - Computation of large invariant subspaces using polynomial filtered lanczos iterations with applications in density functional theory.

N2 - 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. AB - 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.

### Invariant Subspaces of Matrices with Applications

Computer Science and Engineering. Abstract 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. Fingerprint Lanczos. Invariant Subspace. Density Functional. Lanczos Algorithm. Smallest Eigenvalue. Orthogonal Basis.

Materials Science. Low-pass Filter. Cross product. View via Publisher.