✦ LIBER ✦

Systematic sparse matrix error control for linear scaling electronic structure calculations

✍ Scribed by Emanuel H. Rubensson; Paweł Sałek

Publisher: John Wiley and Sons
Year: 2005
Tongue: English
Weight: 312 KB
Volume: 26
Category: Article
ISSN: 0192-8651
DOI: 10.1002/jcc.20315

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

Efficient truncation criteria used in multiatom blocked sparse matrix operations for ab initio calculations are proposed. As system size increases, so does the need to stay on top of errors and still achieve high performance. A variant of a blocked sparse matrix algebra to achieve strict error control with good performance is proposed. The presented idea is that the condition to drop a certain submatrix should depend not only on the magnitude of that particular submatrix, but also on which other submatrices that are dropped. The decision to remove a certain submatrix is based on the contribution the removal would cause to the error in the chosen norm. We study the effect of an accumulated truncation error in iterative algorithms like trace correcting density matrix purification. One way to reduce the initial exponential growth of this error is presented. The presented error control for a sparse blocked matrix toolbox allows for achieving optimal performance by performing only necessary operations needed to maintain the requested level of accuracy. © 2005 Wiley Periodicals, Inc. J Comput Chem 26: 1628–1637, 2005

📜 SIMILAR VOLUMES

Bringing about matrix sparsity in linear

Bringing about matrix sparsity in linear-scaling electronic structure calculations

✍ Emanuel H. Rubensson; Elias Rudberg 📂 Article 📅 2011 🏛 John Wiley and Sons 🌐 English ⚖ 790 KB

The performance of linear-scaling electronic structure calculations depends critically on matrix sparsity. This article gives an overview of different strategies for removal of small matrix elements, with emphasis on schemes that allow for rigorous control of errors. In particular, a novel scheme is

Sparse matrix multiplications for linear

Sparse matrix multiplications for linear scaling electronic structure calculations in an atom-centered basis set using multiatom blocks

✍ Chandra Saravanan; Yihan Shao; Roi Baer; Philip N. Ross; Martin Head–Gordon 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 92 KB

## Abstract A sparse matrix multiplication scheme with multiatom blocks is reported, a tool that can be very useful for developing linear‐scaling methods with atom‐centered basis functions. Compared to conventional element‐by‐element sparse matrix multiplication schemes, __efficiency is gained__ by

A hierarchic sparse matrix data structur

A hierarchic sparse matrix data structure for large-scale Hartree-Fock/Kohn-Sham calculations

✍ Emanuel H. Rubensson; Elias Rudberg; Paweł Sałek 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 597 KB

## Abstract A hierarchic sparse matrix data structure for Hartree‐Fock/Kohn‐Sham calculations is presented. The data structure makes the implementation of matrix manipulations needed for large systems faster, easier, and more maintainable without loss of performance. Algorithms for symmetric matrix