Related papers: Minimal Polynomial and Reduced Rank Extrapolation …
Reduced Rank Extrapolation (RRE) is a polynomial type method used to accelerate the convergence of sequences of vectors $\{\boldsymbol{x}_m\}$. It is applied successfully in different disciplines of science and engineering in the solution…
An important problem that arises in different areas of science and engineering is that of computing the limits of sequences of vectors $\{\xx_m\}$, where $\xx_m\in \C^N$, $N$ being very large. Such sequences arise, for example, in the…
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a…
In this paper, we present a new framework for the recent multidimensional extrapolation methods: Tensor Global Minimal Polynomial (TG-MPE) and Tensor Global Reduced Rank Extrapolation (TG-RRE) methods. We develop a new approach to the one…
We investigate the acceleration of stationary iterations for multi-term Sylvester equation by means of reduced rank extrapolation (RRE). Theoretical convergence results and implementations are provided for both small and large-scale…
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value…
In this work, we study the application the classical Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for solving initial-value problems of systems of ordinary…
Monotone systems of polynomial equations (MSPEs) are systems of fixed-point equations $X_1 = f_1(X_1, ..., X_n),$ $..., X_n = f_n(X_1, ..., X_n)$ where each $f_i$ is a polynomial with positive real coefficients. The question of computing…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
While high-dimensional embedding vectors are being increasingly employed in various tasks like Retrieval-Augmented Generation and Recommendation Systems, popular dimensionality reduction (DR) methods such as PCA and UMAP have rarely been…
Standard multiparameter eigenvalue problems (MEPs) are systems of $k\ge 2$ linear $k$-parameter square matrix pencils. Recently, a new form of multiparameter eigenvalue problems has emerged: a rectangular MEP (RMEP) with only one…
The rectangular multiparameter eigenvalue problem (RMEP) involves rectangular coefficient matrices (usually with more rows than columns) and may potentially have no solution in its original form. A minimal perturbation framework is proposed…
Relative positional embeddings (RPE) have received considerable attention since RPEs effectively model the relative distance among tokens and enable length extrapolation. We propose KERPLE, a framework that generalizes relative position…
Multimodal relation extraction (MRE) is a crucial task in the fields of Knowledge Graph and Multimedia, playing a pivotal role in multimodal knowledge graph construction. However, existing methods are typically limited to extracting a…
Most Relevant Explanation (MRE) is a method for finding multivariate explanations for given evidence in Bayesian networks [12]. This paper studies the theoretical properties of MRE and develops an algorithm for finding multiple top MRE…
Recently, prompt-tuning with pre-trained language models (PLMs) has demonstrated the significantly enhancing ability of relation extraction (RE) tasks. However, in low-resource scenarios, where the available training data is scarce,…
Mixture proportion estimation (MPE) is the problem of estimating the weight of a component distribution in a mixture, given samples from the mixture and component. This problem constitutes a key part in many "weakly supervised learning"…
We propose a new method for low-rank approximation of Moore-Penrose pseudoinverses (MPPs) of large-scale matrices using tensor networks. The computed pseudoinverses can be useful for solving or preconditioning of large-scale overdetermined…
With the development of feature extraction technique, one sample always can be represented by multiple features which locate in high-dimensional space. Multiple features can re ect various perspectives of one same sample, so there must be…
The Mutual Reinforcement Effect (MRE) investigates the synergistic relationship between word-level and text-level classifications in text classification tasks. It posits that the performance of both classification levels can be mutually…