1 citations · 1 across the 12 of their papers we have counts for
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Attention Mechanisms Through the Lens of Numerical Methods: Approximation Methods and Alternative Formulations
Michel Fabrice Serret, Alice Cortinovis, Yijun Dong +10
The attention mechanism is the computational core of modern Transformer architectures, but its quadratic complexity in the input sequence length is the bottleneck for large-scale i…
Detecting when one probe vector is enough for preconditioned log-determinant approximation
Alice Cortinovis, Daniele Toni
We present randomized algorithms for estimating the log-determinant of regularized symmetric positive semi-definite matrices. The algorithms access the matrix only through matrix v…
Adaptive randomized pivoting for column subset selection, DEIM, and low-rank approximation
Alice Cortinovis, Daniel Kressner
We derive a new adaptive leverage score sampling strategy for solving the Column Subset Selection Problem (CSSP). The resulting algorithm, called Adaptive Randomized Pivoting, can…
Improved bounds for randomized Schatten norm estimation of numerically low-rank matrices
Ya-Chi Chu, Alice Cortinovis
In this work, we analyze the variance of a stochastic estimator for computing Schatten norms of matrices. The estimator extracts information from a single sketch of the matrix, tha…
A sublinear-time randomized algorithm for column and row subset selection based on strong rank-revealing QR factorizations
Alice Cortinovis, Lexing Ying
In this work, we analyze a sublinear-time algorithm for selecting a few rows and columns of a matrix for low-rank approximation purposes. The algorithm is based on an initial unifo…
Computing Free Convolutions via Contour Integrals
Alice Cortinovis, Lexing Ying
This work proposes algorithms for computing additive and multiplicative free convolutions of two given measures. We consider measures with compact support whose free convolution re…
Speeding up Krylov subspace methods for computing f(A)b via randomization
Alice Cortinovis, Daniel Kressner, Yuji Nakatsukasa
This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A…
Improved variants of the Hutch++ algorithm for trace estimation
David Persson, Alice Cortinovis, Daniel Kressner
This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ co…
Divide and conquer methods for functions of matrices with banded or hierarchical low-rank structure
Alice Cortinovis, Daniel Kressner, Stefano Massei
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer m…
Low-rank updates of matrix functions II: Rational Krylov methods
Bernhard Beckermann, Alice Cortinovis, Daniel Kressner +1
This work develops novel rational Krylov methods for updating a large-scale matrix function f(A) when A is subject to low-rank modifications. It extends our previous work in this c…
On randomized trace estimates for indefinite matrices with an application to determinants
Alice Cortinovis, Daniel Kressner
Randomized trace estimation is a popular and well studied technique that approximates the trace of a large-scale matrix by computing the average of for many samples of…
Low-rank approximation in the Frobenius norm by column and row subset selection
Alice Cortinovis, Daniel Kressner
A CUR approximation of a matrix is a particular type of low-rank approximation , where and consist of columns and rows of , respectively. One way to…
On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices
Alice Cortinovis, Daniel Kressner, Stefano Massei
The problem of finding a submatrix of maximum volume of a matrix is of interest in a variety of applications. For example, it yields a quasi-best low-rank approxim…