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Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image…
Under the hypothesis that the deviations of the desired eigenvectors of the matrix $A$ from the underlying subspace tend to zero, the Ritz vectors may not converge and have poor or little accuracy. This phenomenon is not unusual and…
Image segmentation is a popular area of research in computer vision that has many applications in automated image processing. A recent technique called piecewise flat embeddings (PFE) has been proposed for use in image segmentation; PFE…
The adoption of hybrid GPU-CPU nodes in traditional supercomputing platforms opens acceleration opportunities for electronic structure calculations in materials science and chemistry applications, where medium sized Hermitian generalized…
One of the most popular and important first-order iterations that provides optimal complexity of the classical proximal gradient method (PGM) is the "Fast Iterative Shrinkage/Thresholding Algorithm" (FISTA). In this paper, two inexact…
Plaintext-ciphertext matrix multiplication (PC-MM) is an indispensable tool in privacy-preserving computations such as secure machine learning and encrypted signal processing. While there are many established algorithms for…
Applications related to artificial intelligence, machine learning, and system identification simulations essentially use eigenvectors. Calculating eigenvectors for very large matrices using conventional methods is compute-intensive and…
Fully Homomorphic Encryption (FHE) is a technique that allows arbitrary computations to be performed on encrypted data without the need for decryption, making it ideal for securing many emerging applications. However, FHE computation is…
In this paper, we present and analyze a new set of low-rank recovery algorithms for linear inverse problems within the class of hard thresholding methods. We provide strategies on how to set up these algorithms via basic ingredients for…
Parameter-Efficient Fine-Tuning (PEFT) has become a key strategy for adapting large language models, with recent advances in sparse tuning reducing overhead by selectively updating key parameters or subsets of data. Existing approaches…
Several problems in machine learning, statistics, and other fields rely on computing eigenvectors. For large scale problems, the computation of these eigenvectors is typically performed via iterative schemes such as subspace iteration or…
Partitioning the vertices of a (hyper)graph into k roughly balanced blocks such that few (hyper)edges run between blocks is a key problem for large-scale distributed processing. A current trend for partitioning huge (hyper)graphs using low…
In the "Big Data" era, a lot of data must be processed and moved between processing and memory units. New technologies and architectures have emerged to improve system performance and overcome the memory bottleneck. The memristor is a…
This paper focuses on scalability and robustness of spectral clustering for extremely large-scale datasets with limited resources. Two novel algorithms are proposed, namely, ultra-scalable spectral clustering (U-SPEC) and ultra-scalable…
The fortran version of the AcerDET package has been published in [1], and used in the multiple publications on the predictions for physics at LHC. The package provides, starting from list of particles in the event, the list of reconstructed…
Non-smoothness at optimal points is a common phenomenon in many eigenvalue optimization problems. We consider two recent algorithms to minimize the largest eigenvalue of a Hermitian matrix dependent on one parameter, both proven to be…
An adaptive refinement strategy, based on an equilibrated flux a posteriori error estimator, is proposed in the context of defeaturing problems. Defeaturing consists of removing features from complex domains to simplify mesh generation and…
We study randomized sketching methods for approximately solving least-squares problem with a general convex constraint. The quality of a least-squares approximation can be assessed in different ways: either in terms of the value of the…
The ratio between two probability density functions is an important component of various tasks, including selection bias correction, novelty detection and classification. Recently, several estimators of this ratio have been proposed. Most…
This paper presents enhancement strategies for the Hermitian and skew-Hermitian splitting method based on gradient iterations. The spectral properties are exploited for the parameter estimation, often resulting in a better convergence. In…