Related papers: Algorithms in the classical N\'eron Desingularizat…

In a previous paper, we described a computer program called Qubiter which can decompose an arbitrary unitary matrix into elementary operations of the type used in quantum computation. In this paper, we describe a method of reducing the…

We construct reversible Boolean circuits efficiently simulating reversible Turing machines. Both the circuits and the simulation proof are rather simple. Then we give a fairly straightforward generalization of the circuits and the…

This chapter studies the problem of decomposing a tensor into a sum of constituent rank one tensors. While tensor decompositions are very useful in designing learning algorithms and data analysis, they are NP-hard in the worst-case. We will…

Most elementary numerical schemes found useful for solving classical trajectory problems are {\it canonical transformations}. This fact should be make more widely known among teachers of computational physics and Hamiltonian mechanics. From…

This paper proposes fast randomized algorithms for computing the Kronecker Tensor Decomposition (KTD). The proposed algorithms can decompose a given tensor into the KTD format much faster than the existing state-of-the-art algorithms. Our…

We describe an algorithm for the computation of generalized (or weighted) Ehrhart series based on Stanley decompositions as implemented in the offspring NmzIntegrate of Normaliz. The algorithmic approach includes elementary proofs of the…

We give a general method for rounding linear programs that combines the commonly used iterated rounding and randomized rounding techniques. In particular, we show that whenever iterated rounding can be applied to a problem with some slack,…

We present a construction, rendered in Quipper, of a quantum algorithm which probabilistically computes a classical function from n bits to n bits. The construction is intended to be of interest primarily for the features of Quipper it…

The purpose of this note is to extend the divergences analyzed in a previous work by application of the Deformed Logarithm in its most general form. In a study on entropic divergences, we have analyzed the different forms of the deformed…

We propose an algorithm generating planar networks which structure resembles a hierarchical structure of desiccation crack patterns.

Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both…

In this note, we use a natural desingularization of the conormal variety of the variety of n x n symmetric matrices of rank at most r to find a general formula for the algebraic degree in semidefinite programming.

This paper surveys randomized algorithms in numerical linear algebra for low-rank decompositions of matrices and tensors. The survey begins with a review of classical matrix algorithms that can be accelerated by randomized dimensionality…

Our main result establishes functorial desingularization of noetherian quasi-excellent schemes over $\bfQ$ with ordered boundaries. A functorial embedded desingularization of quasi-excellent schemes of characteristic zero is deduced.…

Desingularization is the problem of finding a left multiple of a given Ore operator in which some factor of the leading coefficient of the original operator is removed. An order-degree curve for a given Ore operator is a curve in the…

While it seems possible that quantum computers may allow for algorithms offering a computational speed-up over classical algorithms for some problems, the issue is poorly understood. We explore this computational speed-up by investigating…

We develop the symplectic elimnation algorithm. This algorithm using simple row operations reduce a symplectic matrix to a diagonal matrix. This algorithm gives rise to a decomposition of an arbitrary matrix into a product of a symplectic…

We develop a correspondence between the theory of sequential algorithms and classical reasoning, via Kreisel's no-counterexample interpretation. Our framework views realizers of the no-counterexample interpretation as dynamic processes…

A simplicial set is said to be non-singular if the representing map of each non-degenerate simplex is degreewise injective. The inclusion into the category of simplicial sets, of the full subcategory whose objects are the non-singular…

Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…