Related papers: Recursive blocked algorithms for linear systems wi…
In this paper, we consider the challenge of reconstructing jointly sparse vectors from linear measurements. Firstly, we show that by utilizing the rank of the output data matrix we can reduce the problem to a full column rank case. This…
This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the…
Building on the previous work of Lee et al. and Ferdinand et al. on coded computation, we propose a sequential approximation framework for solving optimization problems in a distributed manner. In a distributed computation system, latency…
Recursive list decoding of Reed-Muller (RM) codes, with moderate list size, is known to approach maximum-likelihood (ML) performance of short length $(\leq 256)$ RM codes. Recursive decoding employs the Plotkin construction to split the…
In this paper, we further investigate and refine the subspace-constrained preconditioning technique to enhance the theoretical and numerical convergence properties of randomized iterative methods for solving linear systems. In particular,…
A class of restarted randomized surrounding methods are presented to accelerate the surrounding algorithms by restarted techniques for solving the linear equations. Theoretical analysis prove that the proposed method converges under the…
We present several generative and predictive algorithms based on the RKHS (reproducing kernel Hilbert spaces) methodology, which, most importantly, are scale up efficiently with large datasets or high-dimensional data. It is well recognized…
We introduce a predictor-corrector discretisation scheme for the numerical integration of a class of stochastic differential equations and prove that it converges with weak order 1.0. The key feature of the new scheme is that it builds up…
In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…
We consider integer and linear programming problems for which the linear constraints exhibit a (recursive) block-structure: The problem decomposes into independent and efficiently solvable sub-problems if a small number of constraints is…
Block coordinate descent (BCD) methods are prevalent in large scale optimization problems due to the low memory and computational costs per iteration, the predisposition to parallelization, and the ability to exploit the structure of the…
Computation of the spherical harmonic rotation coefficients or elements of Wigner's d-matrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods…
Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
We present an algorithm that can efficiently compute a broad class of inferences for discrete-time imprecise Markov chains, a generalised type of Markov chains that allows one to take into account partially specified probabilities and other…
Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…
In this paper, we propose and analyze the numerical algorithms for fast solution of periodic elliptic problems in random media in $\mathbb{R}^d$, $d=2,3$. We consider the stochastic realizations using checkerboard configuration of the…
This paper considers the numerical solution of generalized Sylvester matrix equations, which arise in many scientific and engineering applications but remain challenging to solve efficiently, particularly when the coefficient matrices are…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
In this paper, a class of optimization problems with nonlinear inequality constraints is discussed. Based on the ideas of sequential quadratic programming algorithm and the method of strongly sub-feasible directions, a new superlinearly…