Related papers: Kaltofen's division-free determinant algorithm dif…
This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for…
We propose a new algorithm to solve optimization problems of the form $\min f(X)$ for a smooth function $f$ under the constraints that $X$ is positive semidefinite and the diagonal blocks of $X$ are small identity matrices. Such problems…
As more and more multiphysics effects are entering the field of CFD simulations, this raises the question how they can be accurately captured in gradient computations for shape optimization. The latter has been successfully enriched over…
Least squares form one of the most prominent classes of optimization problems, with numerous applications in scientific computing and data fitting. When such formulations aim at modeling complex systems, the optimization process must…
Karppa & Kaski (2019) proposed a novel ``broken" or ``opportunistic" matrix multiplication algorithm, based on a variant of Strassen's algorithm, and used this to develop new algorithms for Boolean matrix multiplication, among other tasks.…
The idea of embedding optimization problems into deep neural networks as optimization layers to encode constraints and inductive priors has taken hold in recent years. Most existing methods focus on implicitly differentiating…
In this work, multi-variable derivative-free optimization algorithms for unconstrained optimization problems are developed. A novel procedure for approximating the gradient of multi-variable objective functions based on non-commutative maps…
We study faster algorithms for producing the minimum degree ordering used to speed up Gaussian elimination. This ordering is based on viewing the non-zero elements of a symmetric positive definite matrix as edges of an undirected graph, and…
The binary-forking model is a parallel computation model, formally defined by Blelloch et al. very recently, in which a thread can fork a concurrent child thread, recursively and asynchronously. The model incurs a cost of $\Theta(\log n)$…
We present the asymptotically fastest known algorithms for some basic problems on univariate polynomial matrices: rank, nullspace, determinant, generic inverse, reduced form. We show that they essentially can be reduced to two computer…
In this paper we present two algorithms for the computation of a diagonal form of a matrix over non-commutative Euclidean domain over a field with the help of Gr\"obner bases. This can be viewed as the pre-processing for the computation of…
Determinantal Point Processes (DPPs) are probabilistic models that arise in quantum physics and random matrix theory and have recently found numerous applications in computer science. DPPs define distributions over subsets of a given ground…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
Recently, reinforcement algorithms discovered new algorithms that really jump-started a wave of excitements and a flourishing of publications. However, there is little on implementations, applications, and, especially, no absolute…
In this note we translate the pictorial description of Gulotta's efficient inverse algorithm (arXiv:0807.3012) into matrix operations, so that it can be implemented on a computer. As an application we point out that this in combination with…
Recent work of Belinschi, Mai and Speicher resulted in a general algorithm to calculate the distribution of any selfadjoint polynomial in free variables. Since many classes of independent random matrices become asymptotically free if the…
The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…
Multiplying matrices is among the most fundamental and compute-intensive operations in machine learning. Consequently, there has been significant work on efficiently approximating matrix multiplies. We introduce a learning-based algorithm…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Inference and simulation in the context of high-dimensional dynamical systems remain computationally challenging problems. Some form of dimensionality reduction is required to make the problem tractable in general. In this paper, we propose…