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Efficient linear algebra routines for symmetric matrices stored in packed form
Reinhart Ahlrichs1, Kakha Tsereteli
1Lehrstuhl für Theoretische Chemie, Institut für Physikalische Chemie, Universität Karlsruhe, Germany. reinhart.ahlrichs@chemie.uni-karlsruhe.de
Journal of Computational Chemistry
|April 2, 2002
Summary
This study introduces efficient linear algebra routines for symmetric matrices, crucial for quantum chemistry calculations. These optimized methods reduce computational demands and memory usage in scientific computing.
Area of Science:
- Quantum chemistry
- Computational physics
- Applied mathematics
Background:
- Quantum chemistry computations frequently utilize linear algebra routines.
- Symmetric matrices are fundamental in quantum chemistry, requiring operations like diagonalization and Cholesky decomposition.
- Existing methods can be computationally intensive and memory-demanding.
Purpose of the Study:
- To present a concise set of basic linear algebra routines tailored for symmetric matrices.
- To enhance the efficiency of quantum chemistry calculations.
- To minimize memory footprint in numerical simulations.
Main Methods:
- Development of optimized algorithms for matrix diagonalization.
- Implementation of efficient Cholesky decomposition for positive definite matrices.
- Focus on routines with minimal memory requirements.
Main Results:
- A small, highly efficient set of linear algebra routines for symmetric matrices.
- Demonstrated reduction in computational time for key quantum chemistry tasks.
- Significant decrease in memory usage compared to standard implementations.
Conclusions:
- The presented routines offer a practical improvement for quantum chemistry software.
- Efficiency gains and memory minimization are critical for large-scale simulations.
- These optimized methods support more complex and extensive quantum mechanical calculations.