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Abstract: In this paper, we present an algorithm for computing a partial sum of eigenvalues of a large symmetric positive definite matrix pair. We show that this computational task is intimately connected to compute a bilinear form u T f(A)u for a properly defined matrix A, a vector u and a function f(\Delta). Compared to existing techniques which compute individual eigenvalues and then sum them up, the new algorithm is generally less accurate, but requires significantly less memory and CPU time. In... (Update)
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...intractable large scale problems. The relative accuracy of new approach within 0.4 to 1. 5 is satisfactory for the application [3]. 30 20 10 0 10 20 30 Spectrum Fig. 3. A carbon cluster that forms part of a knee structure, and the corresponding spectrum Table 3....
...1= t ) and f(t) exp(fft) where and ff are given constants. In a sequence of papers Golub and collaborators, see, e.g. [1, 2, 3, 4, 5, 7], have exploited the connection between matrix functionals of the form (1) Stieltjes integrals, Gauss type quadrature rules and...
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BibTeX entry: (Update)
Bai, Z., Fahey, M., Golub, G., Menon, M., Richter, E.: Computing partial eigenvalue sum in electronic structure calculations, Scientific Computing and Computational Mathematics Program, Computer Science Dept., Stanford University, SCCM-98-03, 1998. http://citeseer.ist.psu.edu/article/bai97computing.html More
@misc{ bai98computing,
author = "Z. Bai and M. Fahey and G. Golub and M. Menon and E. Richter",
title = "Computing partial eigenvalue sum in electronic structure calculations",
text = "Bai, Z., Fahey, M., Golub, G., Menon, M., Richter, E.: Computing partial
eigenvalue sum in electronic structure calculations, Scientific Computing
and Computational Mathematics Program, Computer Science Dept., Stanford
University, SCCM-98-03, 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/article/bai97computing.html" }
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