<ul><li>Researchers have developed a new class of preconditioned iterative methods for solving linear systems, resulting in faster runtimes for various linear algebraic problems.</li><li>The methods involve constructing a low-rank Nyström approximation to the matrix using sparse random matrix sketching.</li><li>The approximation is then used to create a preconditioner, which is inverted quickly using additional levels of random sketching and preconditioning.</li><li>The research proves the convergence of the methods is dependent on the average condition number of the matrix, which improves as the rank of the Nyström approximation increases.</li></ul>

Faster Linear Systems and Matrix Norm Approximation via Multi-level Sketched Preconditioning

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