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A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...
The locally optimal block preconditioned conjugate gradient (LOBPCG) algorithm is a popular approach for computing a few smallest eigenvalues and the corresponding eigenvectors of a large Hermitian positive definite matrix A. In this work, we propose a mix ...
The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over the Riemannian ma ...
In this thesis we address the computation of a spectral decomposition for symmetric
banded matrices. In light of dealing with large-scale matrices, where classical dense
linear algebra routines are not applicable, it is essential to design alternative tech ...
In this paper, comprehensive pulsar-based Guidance, Navigation and Control (GNC) system is designed and applied to satellites formation flying. The complete autonomy of the X-ray pulsar navigation technology provides both absolute and relative positioning ...
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Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...
Euclidean distance matrices (EDMs) are matrices of the squared distances between points. The definition is deceivingly simple; thanks to their many useful properties, they have found applications in psychometrics, crystallography, machine learning, wireles ...
Modern positioning technologies enable collecting trajectories from moving objects across different locations over time, typically containing time-varying measurement errors of positioning systems. Unfortunately, current models on uncertain trajectories ar ...
Biomaterials such as structure proteins are constructed from limited sets of chemical building blocks and supramolecular motifs. Nevertheless, they exhibit extraordinary properties specifically tailored for a broad range of applications because hierarchica ...
