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Fast Sparse Cholesky Decomposition and Inversion using Nested Dissection Matrix Reordering

https://doi.org/10.1021/ct100618s
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Ab Initio NMR Spectra for Molecular Systems with a Thousand and More Atoms: A Linear‐Scaling Method
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Ab Initio NMR Spectra for Molecular Systems with a Thousand and More Atoms: A Linear‐Scaling Method
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Linear‐scaling Cholesky decomposition
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Simplifications in the generation and transformation of two‐electron integrals in molecular calculations
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Application of cholesky‐like matrix decomposition methods to the evaluation of atomic orbital integrals and integral derivatives
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Cholesky factorization
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An Evaluation of Sparse Direct Symmetric Solvers: An Introduction and Preliminary Findings
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Predicting Structure in Nonsymmetric Sparse Matrix Factorizations
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An algorithm to compute a sparse basis of the null space
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Task scheduling for parallel sparse Cholesky factorization
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Zum Hilbertschen Aufbau der reellen Zahlen
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A linear time implementation of the reverse Cuthill-McKee algorithm
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On the Beebe-Linderberg two-electron integral approximation
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Computation of cubic harmonics
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On the Householder-Fox algorithm for decomposing a projection
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Rank and null space calculations using matrix decomposition without column interchanges
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A parallel algorithm for sparse symbolic Cholesky factorization on a multiprocessor
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Reordering sparse matrices for parallel elimination
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Parallel nested dissection
inferredcites →https://doi.org/10.1016/0377-0427(87)90199-3openalex-snapshot
Detection of near-singularity in Cholesky and LDLT factorizations
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Computer Organization and Design
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Quartic scaling evaluation of canonical scaled opposite spin second-order Møller–Plesset correlation energy using Cholesky decompositions
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Solving unsymmetric sparse systems of linear equations with PARDISO
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Constructing a minimum height elimination tree of a tree in linear time
inferredcites →https://doi.org/10.1016/j.laa.2007.11.025openalex-snapshot
Block computation and representation of a sparse nullspace basis of a rectangular matrix
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Geometry optimization methods for modeling large molecules
inferredcites →https://doi.org/10.1016/s0009-2614(00)00814-9openalex-snapshot
Direct optimization of the AO density matrix in Hartree–Fock and Kohn–Sham theories
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A reformulation of the coupled perturbed self-consistent field equations entirely within a local atomic orbital density matrix-based scheme
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A generalized inverse for matrices
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FUNCTIONAL PEARL On building trees with minimum height
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Auxiliary Density Matrix Methods for Hartree−Fock Exchange Calculations
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Cholesky Decomposition-Based Multiconfiguration Second-Order Perturbation Theory (CD-CASPT2): Application to the Spin-State Energetics of CoIII(diiminato)(NPh)
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Linear Scaling Density Functional Calculations with Gaussian Orbitals
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Advances in methods and algorithms in a modern quantum chemistry program package
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Direct optimization of the atomic-orbital density matrix using the conjugate-gradient method with a multilevel preconditioner
inferredcites →https://doi.org/10.1063/1.1558476openalex-snapshot
Curvy steps for density matrix-based energy minimization: Application to large-scale self-consistent-field calculations
inferredcites →https://doi.org/10.1063/1.1578621openalex-snapshot
Reduced scaling in electronic structure calculations using Cholesky decompositions
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An exact reformulation of the diagonalization step in electronic structure calculations as a set of second order nonlinear equations
inferredcites →https://doi.org/10.1063/1.1809602openalex-snapshot
Scaled opposite-spin second order Møller–Plesset correlation energy: An economical electronic structure method
inferredcites →https://doi.org/10.1063/1.2360264openalex-snapshot
Fast noniterative orbital localization for large molecules
inferredcites →https://doi.org/10.1063/1.2709881openalex-snapshot
Linear-scaling symmetric square-root decomposition of the overlap matrix
inferredcites →https://doi.org/10.1063/1.2736701openalex-snapshot
Low-cost evaluation of the exchange Fock matrix from Cholesky and density fitting representations of the electron repulsion integrals
inferredcites →https://doi.org/10.1063/1.2749509openalex-snapshot
Linear-scaling method for calculating nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals within Hartree-Fock and density-functional theory
inferredcites →https://doi.org/10.1063/1.2777146openalex-snapshot
Unbiased auxiliary basis sets for accurate two-electron integral approximations
inferredcites →https://doi.org/10.1063/1.2794033openalex-snapshot
A density matrix-based method for the linear-scaling calculation of dynamic second- and third-order properties at the Hartree-Fock and Kohn-Sham density functional theory levels
inferredcites →https://doi.org/10.1063/1.2925269openalex-snapshot
Cholesky decomposition of the two-electron integral matrix in electronic structure calculations
inferredcites →https://doi.org/10.1063/1.2955755openalex-snapshot
Analytic derivatives for the Cholesky representation of the two-electron integrals
inferredcites →https://doi.org/10.1063/1.2988315openalex-snapshot
Method specific Cholesky decomposition: Coulomb and exchange energies
inferredcites →https://doi.org/10.1063/1.3116103openalex-snapshot
Approximated electron repulsion integrals: Cholesky decomposition versus resolution of the identity methods
inferredcites →https://doi.org/10.1063/1.3116784openalex-snapshot
Atomic Cholesky decompositions: A route to unbiased auxiliary basis sets for density fitting approximation with tunable accuracy and efficiency
inferredcites →https://doi.org/10.1063/1.3142592openalex-snapshot
Cholesky-decomposed densities in Laplace-based second-order Møller–Plesset perturbation theory
inferredcites →https://doi.org/10.1063/1.3315419openalex-snapshot
Cholesky decomposition within local multireference singles and doubles configuration interaction
inferredcites →https://doi.org/10.1063/1.473579openalex-snapshot
Linear scaling conjugate gradient density matrix search as an alternative to diagonalization for first principles electronic structure calculations
inferredcites →https://doi.org/10.1063/1.474404openalex-snapshot
Semiempirical methods with conjugate gradient density matrix search to replace diagonalization for molecular systems containing thousands of atoms
inferredcites →https://doi.org/10.1063/1.475423openalex-snapshot
A tensor formulation of many-electron theory in a nonorthogonal single-particle basis
inferredcites →https://doi.org/10.1063/1.476927openalex-snapshot
Comparison of conjugate gradient density matrix search and Chebyshev expansion methods for avoiding diagonalization in large-scale electronic structure calculations
inferredcites →https://doi.org/10.1063/1.477969openalex-snapshot
A simplified density matrix minimization for linear scaling self-consistent field theory
inferredcites →https://doi.org/10.1063/1.478008openalex-snapshot
What is the best alternative to diagonalization of the Hamiltonian in large scale semiempirical calculations?
inferredcites →https://doi.org/10.1080/00268970210158722openalex-snapshot
Curvy steps for density matrix based energy minimization: tensor formulation and toy applications
inferredcites →https://doi.org/10.1103/physrevb.47.10891openalex-snapshot
Density-matrix electronic-structure method with linear system-size scaling
inferredcites →https://doi.org/10.1103/physrevb.50.17611openalex-snapshot
Generalization of the density-matrix method to a nonorthogonal basis
inferredcites →https://doi.org/10.1109/proc.1967.6011openalex-snapshot
Direct solutions of sparse network equations by optimally ordered triangular factorization
inferredcites →https://doi.org/10.1137/0201010openalex-snapshot
Depth-First Search and Linear Graph Algorithms
inferredcites →https://doi.org/10.1137/0205021openalex-snapshot
Algorithmic Aspects of Vertex Elimination on Graphs
inferredcites →https://doi.org/10.1137/0209044openalex-snapshot
An Optimal Agorithm for Symbolic Factorization of Symmetric Matrices
inferredcites →https://doi.org/10.1137/0213035openalex-snapshot
Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs
inferredcites →https://doi.org/10.1137/050638369openalex-snapshot
On the Computation of Null Spaces of Sparse Rectangular Matrices
inferredcites →https://doi.org/10.1137/0602010openalex-snapshot
Computing the Minimum Fill-In is NP-Complete
inferredcites →https://doi.org/10.1137/0611010openalex-snapshot
The Role of Elimination Trees in Sparse Factorization
inferredcites →https://doi.org/10.1137/0613078openalex-snapshot
Rank Detection Methods for Sparse Matrices
inferredcites →https://doi.org/10.1137/0614019openalex-snapshot
On Finding Supernodes for Sparse Matrix Computations
inferredcites →https://doi.org/10.1137/0702016openalex-snapshot
Calculating the Singular Values and Pseudo-Inverse of a Matrix
inferredcites →https://doi.org/10.1137/0710032openalex-snapshot
Nested Dissection of a Regular Finite Element Mesh
inferredcites →https://doi.org/10.1137/0713009openalex-snapshot
Generalizing the Singular Value Decomposition
inferredcites →https://doi.org/10.1137/0909029openalex-snapshot
Equivalent Sparse Matrix Reordering by Elimination Tree Rotations
inferredcites →https://doi.org/10.1137/0910070openalex-snapshot
A Fast Algorithm for Reordering Sparse Matrices for Parallel Factorization
inferredcites →https://doi.org/10.1137/0914048openalex-snapshot
A Supernodal Cholesky Factorization Algorithm for Shared-Memory Multiprocessors
inferredcites →https://doi.org/10.1137/0915009openalex-snapshot
Stability of the Partitioned Inverse Method for Parallel Solution of Sparse Triangular Systems
inferredcites →https://doi.org/10.1137/1031001openalex-snapshot
The Evolution of the Minimum Degree Ordering Algorithm
inferredcites →https://doi.org/10.1137/s0895479800381331openalex-snapshot
On Positive Semidefinite Matrices with Known Null Space
inferredcites →https://doi.org/10.1137/s0895479887139455openalex-snapshot
Predicting Structure in Sparse Matrix Computations
inferredcites →https://doi.org/10.1137/s0895479892236921openalex-snapshot
An Efficient Algorithm to Compute Row and Column Counts for Sparse Cholesky Factorization
inferredcites →https://doi.org/10.1137/s0895479894278952openalex-snapshot
An Approximate Minimum Degree Ordering Algorithm
inferredcites →https://doi.org/10.1137/s0895479897325578openalex-snapshot
Computing the SVD of a General Matrix Product/Quotient
inferredcites →https://doi.org/10.1137/s1064827595287997openalex-snapshot
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
inferredcites →https://doi.org/10.1137/s1064827598339372openalex-snapshot
Orderings for Factorized Sparse Approximate Inverse Preconditioners
inferredcites →https://doi.org/10.1145/103418.103458openalex-snapshot
Wait-free parallel algorithms for the union-find problem
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Anatomy of high-performance matrix multiplication
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High-performance implementation of the level-3 BLAS
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Algorithm 887
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Space and time efficient implementations of parallel nested dissection
inferredcites →https://doi.org/10.1145/1462173.1462176openalex-snapshot
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
inferredcites →https://doi.org/10.1145/214392.214398openalex-snapshot
Modification of the minimum-degree algorithm by multiple elimination
inferredcites →https://doi.org/10.1145/305619.305640openalex-snapshot
Tradeoffs between parallelism and fill in nested dissection
inferredcites →https://doi.org/10.1145/321879.321884openalex-snapshot
Efficiency of a Good But Not Linear Set Union Algorithm
inferredcites →https://doi.org/10.1145/322154.322161openalex-snapshot
Applications of Path Compression on Balanced Trees
inferredcites →https://doi.org/10.1145/602770.602897openalex-snapshot
Improved load distribution in parallel sparse cholesky factorization
inferredcites →https://doi.org/10.1145/602770.602898openalex-snapshot
A scalable parallel algorithm for sparse Cholesky factorization
inferredcites →https://doi.org/10.1145/6497.6499openalex-snapshot
A compact row storage scheme for Cholesky factors using elimination trees
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Reducing the bandwidth of sparse symmetric matrices
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Computer Solution of Large Sparse Positive Definite Systems.
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Scalable parallel sparse LU factorization methods on shared memory multiprocessors

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