Related papers: Polynomial Preconditioners for Regularized Linear …
We introduce a new general purpose multiresolution preconditioner for symmetric linear systems. Most existing multiresolution preconditioners use some standard wavelet basis that relies on knowledge of the geometry of the underlying domain.…
Solving inverse problems requires the knowledge of the forward operator, but accurate models can be computationally expensive and hence cheaper variants that do not compromise the reconstruction quality are desired. This chapter reviews…
The performance of optimization methods is often tied to the spectrum of the objective Hessian. Yet, conventional assumptions, such as smoothness, do often not enable us to make finely-grained convergence statements -- particularly not for…
Recent literature has advocated the use of randomized methods for accelerating the solution of various matrix problems arising throughout data science and computational science. One popular strategy for leveraging randomization is to use it…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Numerous scientific and engineering applications require numerically solving systems of equations. Classically solving a general set of polynomial equations requires iterative solvers, while linear equations may be solved either by direct…
Radial basis functions provide highly useful and flexible interpolants to multivariate functions. Further, they are beginning to be used in the numerical solution of partial differential equations. Unfortunately, their construction requires…
The affine inverse eigenvalue problem consists of identifying a real symmetric matrix with a prescribed set of eigenvalues in an affine space. Due to its ubiquity in applications, various instances of the problem have been widely studied in…
Low rank approximation is a commonly occurring problem in many computer vision and machine learning applications. There are two common ways of optimizing the resulting models. Either the set of matrices with a given rank can be explicitly…
We propose a preconditioner to accelerate the convergence of the GMRES iterative method for solving the system of linear equations obtained from discretize-then-optimize approach applied to optimal control problems constrained by a partial…
Based on the needs of convergence proofs of preconditioned proximal point methods, we introduce notions of partial strong submonotonicity and partial (metric) subregularity of set-valued maps. We study relationships between these two…
This paper investigates a type of fast and flexible preconditioners to solve multilinear system $\mathcal{A}\textbf{x}^{m-1}=\textbf{b}$ with $\mathcal{M}$-tensor $\mathcal{A}$ and obtains some important convergent theorems about…
We present the first framework to solve linear inverse problems leveraging pre-trained latent diffusion models. Previously proposed algorithms (such as DPS and DDRM) only apply to pixel-space diffusion models. We theoretically analyze our…
We study the problem of preconditioning in sequential prediction. From the theoretical lens of linear dynamical systems, we show that convolving the target sequence corresponds to applying a polynomial to the hidden transition matrix.…
Seismic data processing heavily relies on the solution of physics-driven inverse problems. In the presence of unfavourable data acquisition conditions (e.g., regular or irregular coarse sampling of sources and/or receivers), the underlying…
Plug-and-Play Priors (PnP) and Regularisation by Denoising (RED) have established that image denoisers can effectively replace traditional regularisers in linear inverse problem solvers for tasks like super-resolution, demosaicing, and…
The Interior-Point Methods are a class for solving linear programming problems that rely upon the solution of linear systems. At each iteration, it becomes important to determine how to solve these linear systems when the constraint matrix…
There has been a growing interest in parallel strategies for solving trajectory optimization problems. One key step in many algorithmic approaches to trajectory optimization is the solution of moderately-large and sparse linear systems.…
Prior probability models are a fundamental component of many image processing problems, but density estimation is notoriously difficult for high-dimensional signals such as photographic images. Deep neural networks have provided…
Denoiser models have become powerful tools for inverse problems, enabling the use of pretrained networks to approximate the score of a smoothed prior distribution. These models are often used in heuristic iterative schemes aimed at solving…