Related papers: A note on the multiple-recursive matrix method for…
This work is to propose an iterative method of choice to compute a stable subspace of a regular matrix pencil. This approach is to define a sequence of matrix pencils via particular left null spaces. We show that this iteration preserves a…
The trace of a matrix function f(A), most notably of the matrix inverse, can be estimated stochastically using samples< x,f(A)x> if the components of the random vectors x obey an appropriate probability distribution. However such a…
Many nonlinear differential equations arising from practical problems may permit nontrivial multiple solutions relevant to applications, and these multiple solutions are helpful to deeply understand these practical problems and to improve…
In modern neural networks like Transformers, linear layers require significant memory to store activations during backward pass. This study proposes a memory reduction approach to perform backpropagation through linear layers. Since the…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
We present ShapeCrafter, a neural network for recursive text-conditioned 3D shape generation. Existing methods to generate text-conditioned 3D shapes consume an entire text prompt to generate a 3D shape in a single step. However, humans…
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 computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
The aim of our paper is to formulate and solve problems concerning multitime multiple recurrence equations. We discuss in detail the generic properties and the existence and uniqueness of solutions. Among the general things, we discuss in…
We present a proximal gradient method for solving convex multiobjective optimization problems, where each objective function is the sum of two convex functions, with one assumed to be continuously differentiable. The algorithm incorporates…
In this paper, we present a stable and efficient approach for constructing Laguerre pseudospectral differentiation matrices. The proposed method reformulates the off-diagonal entries and computes all required quantities simultaneously using…
The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…
In this paper, we propose a simple yet efficient strategy for improving the multi-objective steepest descent method proposed by Fliege and Svaiter (Math Methods Oper Res, 2000, 3: 479--494). The core idea behind this strategy involves…
We describe a method to construct directed networks from multivariate time series which has several advantages over the widely accepted methods. This method is based on an information theoretic reduction of linear (auto-regressive) models.…
This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…
We present the submatrix method, a highly parallelizable method for the approximate calculation of inverse p-th roots of large sparse symmetric matrices which are required in different scientific applications. We follow the idea of…
Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
A common recent approach to semantic parsing augments sequence-to-sequence models by retrieving and appending a set of training samples, called exemplars. The effectiveness of this recipe is limited by the ability to retrieve informative…
We comment on two randomized algorithms for constructing low-rank matrix decompositions. Both algorithms employ the Subsampled Randomized Hadamard Transform [14]. The first algorithm appeared recently in [9]; here, we provide a novel…