Related papers: SDSL-Solver: Scalable Distributed Sparse Linear So…
This paper proposes a new distributed algorithm for solving linear systems associated with a sparse graph under a generalised diagonal dominance assumption. The algorithm runs iteratively on each node of the graph, with low complexities on…
Diffusion Probabilistic Models (DPMs) are a well-established class of diffusion models for unconditional image generation, while SGMSE+ is a well-established conditional diffusion model for speech enhancement. One of the downsides of…
In practice, non-specialized interior point algorithms often cannot utilize the massively parallel compute resources offered by modern many- and multi-core compute platforms. However, efficient distributed solution techniques are required,…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
Multiplication of a sparse matrix to a dense matrix (SpDM) is widely used in many areas like scientific computing and machine learning. However, existing works under-look the performance optimization of SpDM on modern many-core…
Sparse computations frequently appear in scientific simulations and the performance of these simulations rely heavily on the optimization of the sparse codes. The compact data structures and irregular computation patterns in sparse matrix…
We study the problem of solving semidefinite programs (SDP) in the streaming model. Specifically, $m$ constraint matrices and a target matrix $C$, all of size $n\times n$ together with a vector $b\in \mathbb{R}^m$ are streamed to us…
The matrices used in many computational settings are naturally sparse, holding a small percentage of nonzero elements. Storing such matrices in specialized sparse formats enables algorithms that avoid wasting computation on zeros,…
Sparse matrix multiplication (SpMM) is widely applied to numerous domains, such as graph processing, machine learning, and data analytics. However, inner product based SpMM induces redundant zero-element computing for mismatched nonzero…
In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a…
More than 70% of cloud computing is paid for but sits idle. A large fraction of these idle compute are cheap CPUs with few cores that are not utilized during the less busy hours. This paper aims to enable those CPU cycles to train…
While semidefinite programming (SDP) has traditionally been limited to moderate-sized problems, recent algorithms augmented with matrix sketching techniques have enabled solving larger SDPs. However, these methods achieve scalability at 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…
In this paper we present two strategies to enable "parallelization across the method" for spectral deferred corrections (SDC). Using standard low-order time-stepping methods in an iterative fashion, SDC can be seen as preconditioned Picard…
Speculative decoding is a technique that uses multiple language models to accelerate infer- ence. Previous works have used an experi- mental approach to optimize the throughput of the inference pipeline, which involves LLM training and can…
We establish a new iterative method for solving a class of large and sparse linear systems of equations with three-by-three block coefficient matrices having saddle point structure. Convergence properties of the proposed method are studied…
In this paper, we propose a space-time least-squares isogeometric method to solve parabolic evolution problems, well suited for high-degree smooth splines in the space-time domain. We focus on the linear solver and its computational…
Coupled multi-physics problems are encountered in countless applications and pose significant numerical challenges. Although monolithic approaches offer possibly the best solution strategy, they often require ad-hoc preconditioners and…
In this paper we generalize the Interior Point-Proximal Method of Multipliers (IP-PMM) presented in [An Interior Point-Proximal Method of Multipliers for Convex Quadratic Programming, Computational Optimization and Applications, 78,…
Kernel machines often yield superior predictive performance on various tasks; however, they suffer from severe computational challenges. In this paper, we show how to overcome the important challenge of speeding up kernel machines. In…