Vadym Slyusar
High-performance computing: Developing algorithms and tools for efficient linear algebra computations on large-scale parallel and distributed systems, including multi-core processors, GPUs, and heterogeneous architectures. Tensor computations: Research in this area involves the development of algorithms, models, and computational methods for multidimensional arrays (tensors). Tensors have gained significant attention due to their applications in areas such as machine learning, data science, and quantum computing. Randomized algorithms: Randomized linear algebra algorithms have been gaining traction as they provide fast, approximate solutions to problems. These algorithms often have lower computational complexity than their deterministic counterparts and have applications in machine learning, signal processing, and data analysis. Numerical linear algebra for machine learning: As machine learning and artificial intelligence continue to grow, researchers are developing more efficient linear algebra algorithms and techniques to address the computational challenges of large-scale data processing and deep learning. Graph-based linear algebra: Graphs can be represented as matrices, and linear algebraic techniques can be applied to analyze graph properties. Research in this area includes the development of algorithms for graph sparsification, spectral clustering, and graph signal processing. Quantum computing and linear algebra: Quantum computing offers a different computational paradigm that could revolutionize many areas of science and technology. Linear algebra plays a crucial role in the development of quantum algorithms and the study of quantum systems. Sparsity and low-rank approximation: Exploiting sparsity and low-rank structures can lead to more efficient algorithms for solving large-scale linear algebra problems. Research in this area includes sparse matrix computations, low-rank matrix approximations, and compressed sensing."
Dear Pradip Pansare , I transfer your question to GPT-4 and got such answer: "Some key trends in linear algebra research that were prevalent up to 2021 include:
I'd like to highlight topics 2, 4, 5.
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