Name
Abstract | ||
|---|---|---|
We discuss various applications of trace estimation techniques for evaluating functions of the form tr(f(A)) where f is certain function. The first problem we consider that can be cast in this form is that of approximating the Spectral density or Density of States (DOS) of a matrix. The DOS is a probability density distribution that measures the likelihood of finding eigenvalues of the matrix at a given point on the real line, and it is an important function in solid state physics. We also present a few non- standard applications of spectral densities. Other trace estimation problems we discuss include estimating the trace of a matrix inverse tr(A - 1), the problem of counting eigenvalues and estimating the rank, and approximating the log- determinant (trace of log function). We also discuss a few similar computations that arise in machine learning applications. We review two computationally inexpensive methods to compute traces of matrix functions, namely, the Chebyshev expansion and the Lanczos Quadrature methods. A few numerical examples are presented to illustrate the performances of these methods in different applications. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/978-3-319-97136-0_2 | HIGH PERFORMANCE COMPUTING IN SCIENCE AND ENGINEERING, HPCSE 2017 |
Field | DocType | Volume |
Applied mathematics,Inverse,Lanczos resampling,Matrix (mathematics),Computer science,Matrix function,Parallel computing,Spectral density,Trace (linear algebra),Probability density function,Eigenvalues and eigenvectors | Conference | 11087 |
ISSN | Citations | PageRank |
0302-9743 | 0 | 0.34 |
References | Authors | |
16 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| shashanka ubaru | 1 | 58 | 8.97 |
| Yousef Saad | 2 | 1940 | 254.74 |