Topic
Matrix exponential
About: Matrix exponential is a research topic. Over the lifetime, 1381 publications have been published within this topic receiving 27865 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this article, the exponential of a matrix could be computed in many ways, including approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial.
Abstract: In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...
2,909 citations
TL;DR: Methods involv- ing approximation theory, dierential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed, indicating that some of the methods are preferable to others, but that none are completely satisfactory.
Abstract: In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polyn...
2,454 citations
TL;DR: This work shows that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples, and an exponential speedup is obtained.
Abstract: Supervised machine learning is the classification of new data based on already classified training examples. In this work, we show that the support vector machine, an optimized binary classifier, can be implemented on a quantum computer, with complexity logarithmic in the size of the vectors and the number of training examples. In cases where classical sampling algorithms require polynomial time, an exponential speedup is obtained. At the core of this quantum big data algorithm is a nonsparse matrix exponentiation technique for efficiently performing a matrix inversion of the training data inner-product (kernel) matrix.
1,666 citations
TL;DR: The toolkit provides a set of routines aimed at computing matrix exponentials that computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear OBEs with constant inhomogeneity.
Abstract: Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear OBEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.
948 citations
TL;DR: A new algorithm for computing integrals involving the matrix exponential is given, which employs diagonal Pade approximation with scaling and squaring and is compared with existing techniques.
Abstract: A new algorithm for computing integrals involving the matrix exponential is given. The method employs diagonal Pade approximation with scaling and squaring. Rigorous truncation error bounds are given and incorporated in a Fortran subroutine. The computational aspects of this program are discussed and compared with existing techniques.
939 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 13 |
| 2024 | 21 |
| 2023 | 47 |
| 2022 | 73 |
| 2021 | 76 |
| 2020 | 79 |