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A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…
Mixed linear regression involves the recovery of two (or more) unknown vectors from unlabeled linear measurements; that is, where each sample comes from exactly one of the vectors, but we do not know which one. It is a classic problem, and…
Recent matrix completion based methods have not been able to properly model the Haplotype Assembly Problem (HAP) for noisy observations. To cope with such a case, in this letter we propose a new Minimum Error Correction (MEC) based matrix…
The matrix pencil method is an eigenvalue based approach for the parameter identification of sparse exponential sums. We derive a reconstruction algorithm for multivariate exponential sums that is based on simultaneous diagonalization.…
The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate…
The problem of monotone missing data has been broadly studied during the last two decades and has many applications in different fields such as bioinformatics or statistics. Commonly used imputation techniques require multiple iterations…
We propose NEP_MiniMax, a novel computational method for solving nonlinear eigenvalue problems (NEPs) $T(\lambda)\mathbf{u}= 0$ on compact continua $\Omega \subset \mathbb{C}$. The method combines two key components: (1) a rational minimax…
Polytopal Element Methods (PEM) allow to solve differential equations on general polygonal and polyhedral grids, potentially offering great flexibility to mesh generation algorithms. Differently from classical finite element methods, where…
Constructing fast and accurate surrogate models is a key ingredient for making robust predictions in many topics. We introduce a new model, the Multiparameter Eigenvalue Problem (MEP) emulator. The new method connects emulators and can make…
Multi Expression Programming (MEP) is a Genetic Programming variant which encodes multiple solutions in a single chromosome. This paper introduces and deeply describes several strategies for solving binary and multi-class classification…
The numerical solution of the generalized eigenvalue problem for a singular matrix pencil is challenging due to the discontinuity of its eigenvalues. Classically, such problems are addressed by first extracting the regular part through the…
We present a novel probabilistic finite element method (FEM) for the solution and uncertainty quantification of elliptic partial differential equations based on random meshes, which we call random mesh FEM (RM-FEM). Our methodology allows…
Minimal Polynomial Extrapolation (MPE) and Reduced Rank Extrapolation (RRE) are two polynomial methods used for accelerating the convergence of sequences of vectors $\{{x}_m\}$. They are applied successfully in conjunction with fixed-point…
In this paper, linearly structured partial polynomial inverse eigenvalue problem is considered for the $n\times n$ matrix polynomial of arbitrary degree $k$. Given a set of $m$ eigenpairs ($1 \leqslant m \leqslant kn$), this problem…
When the predicted sequence length exceeds the length seen during training, the transformer's inference accuracy diminishes. Existing relative position encoding methods, such as those based on the ALiBi technique, address the length…
Kernelized maximum-likelihood (ML) expectation maximization (EM) methods have recently gained prominence in PET image reconstruction, outperforming many previous state-of-the-art methods. But they are not immune to the problems of…
The aim of this paper is to propose an efficient adaptive finite element method for eigenvalue problems based on the multilevel correction scheme and inverse power method. This method involves solving associated boundary value problems on…
Eigensolvers involving complex moments can determine all the eigenvalues in a given region in the complex plane and the corresponding eigenvectors of a regular linear matrix pencil. The complex moment acts as a filter for extracting…
LP relaxation-based message passing algorithms provide an effective tool for MAP inference over Probabilistic Graphical Models. However, different LP relaxations often have different objective functions and variables of differing…
Nonlinear eigenvalue problems with eigenvector nonlinearities (NEPv) are algebraic eigenvalue problems whose matrix depends on the eigenvector. Applications range from computational quantum mechanics to machine learning. Due to its…