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Diagonalization of a large matrix is the computational bottleneck in many applications such as electronic structure calculations. We show that a speedup of over 30% can be achieved by exploiting 32-bit floating point operations, while…
A fruitful approach for solving signal deconvolution problems consists of resorting to a frame-based convex variational formulation. In this context, parallel proximal algorithms and related alternating direction methods of multipliers have…
We consider the inverse problem of reconstructing inhomogeneities by performing a finite number of scattering measurements of acoustic type in the time-harmonic setting. We set up the reconstruction as a fully discrete variational problem…
This work is devoted to the homogenization of elliptic equations in high-contrast media in the so-called 'double-porosity' resonant regime, for which we solve two open problems of the literature. First, we prove qualitative stochastic…
We investigate the effects of the regularization procedure used in the J-Matrix method. We show that it influences the convergence, and propose an alternative regularization approach. We explicitly perform some model calculations to…
Measurements are a vital part of any quantum computation, whether as a final step to retrieve results, as an intermediate step to inform subsequent operations, or as part of the computation itself (as in measurement-based quantum…
We present novel, deterministic, efficient algorithms to compute the symmetries of a planar algebraic curve, implicitly defined, and to check whether or not two given implicit planar algebraic curves are similar, i.e. equal up to a…
The task of analytically diagonalizing a tridiagonal matrix can be considerably simplified when a part of the matrix is uniform. Such quasi-uniform matrices occur in several physical contexts, both classical and quantum, where…
This paper examines the properties of real symmetric square matrices with a constant value for the main diagonal elements and another constant value for all off-diagonal elements. This matrix form is a simple subclass of circulant matrices,…
The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…
We show several ways to round a real matrix to an integer one such that the rounding errors in all rows and columns as well as the whole matrix are less than one. This is a classical problem with applications in many fields, in particular,…
Reconstructing the 3D model of a physical object typically requires us to align the depth scans obtained from different camera poses into the same coordinate system. Solutions to this global alignment problem usually proceed in two steps.…
The increasing size of neural networks has led to a growing demand for methods of efficient fine-tuning. Recently, an orthogonal fine-tuning paradigm was introduced that uses orthogonal matrices for adapting the weights of a pretrained…
Geometric numerical integration has recently been exploited to design symplectic accelerated optimization algorithms by simulating the Lagrangian and Hamiltonian systems from the variational framework introduced in Wibisono et al. In this…
In this paper, we are concerned with the stabilization of linear port-Hamiltonian systems of arbitrary order $N \in \mathbb{N}$ on a bounded $1$-dimensional spatial domain $(a,b)$. In order to achieve stabilization, we couple the system to…
In this paper we investigate homogenization results for the principal eigenvalue problem associated to $1$-homogeneous, uniformly elliptic, second-order operators. Under rather general assumptions, we prove that the principal eigenpair…
We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum…
Presented in this paper is a new sparse linear solver methodology motivated by multigrid principles and based around general local transformations that diagonalize a matrix while maintaining its sparsity. These transformations are…
We consider the general form of the linear transformation for point rotation coordinate frames. The frames have the rotation axis at every point. In the transformation the frequency of one frame relative to another is not equivalent to the…
A new generalized matrix inverse is derived which is consistent with respect to arbitrary nonsingular diagonal transformations, e.g., it preserves units associated with variables under state space transformations, thus providing a general…