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Igor Simunec (EPFL)5/18/26, 11:00 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
The randomized Arnoldi process has been used in large-scale scientific computing because it produces a well-conditioned basis for the Krylov subspace more quickly than the standard Arnoldi process. However, the resulting Hessenberg matrix is generally not similar to the one produced by the standard Arnoldi process, which can lead to delays or spike-like irregularities in convergence. In this...
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Emil Krieger (Bergische Universität Wuppertal)5/18/26, 11:25 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Randomized Krylov subspace methods that employ the sketch-and-solve paradigm to substantially reduce orthogonalization cost have recently shown great promise in speeding up computations for many core linear algebra tasks (e.g., solving linear systems, eigenvalue problems and matrix equations, as well as approximating the action of matrix functions on vectors) whenever a nonsymmetric matrix is...
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Mr Bowen Gao (Fudan University)5/18/26, 11:50 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Mixed precision computation has attracted great attention in recent years partly due to the evolution of machine learning and hardware infrastructure. Recent development on mixed precision algorithms has largely enhanced the performance of various linear algebra solvers. In this talk, we propose a mixed precision algorithm for the computation of matrix root functions, primarily the matrix...
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Dr Ritesh Khan5/18/26, 2:00 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Hierarchical matrices or $\mathcal{H}$-matrices are the block low-rank representation of the original matrices and are widely used in fast matrix computations. In this talk, we show that the low-rank blocks of $\mathcal{H}$-matrices can be represented in low precision (precision lower than the working precision) without degrading the overall approximation quality. We provide an explicit rule...
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Xinye Chen (LIP6, CNRS, Sorbonne University)5/18/26, 2:25 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Achieving optimal performance in numerical computations often hinges on aggressively reducing precision or performing rigorous rounding-error analysis to retain numerical accuracy. The precision tuning methods provide a unified, task-specific validation platform for automated precision tuning, enabling a balance between computational efficiency and numerical fidelity. In this talk, we present...
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Takeshi Terao (Waseda University)5/18/26, 2:50 PMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
We consider the eigenvalue problem $Ax^{(i)} = \lambda_i x^{(i)}$ for a real symmetric matrix $A \in \mathbb{R}^{n \times n}$, where $\lambda_i \in \mathbb{R}$ is an eigenvalue of $A$ and $x^{(i)} \in \mathbb{R}^n$ is the corresponding eigenvector. This work investigates iterative refinement methods to improve the accuracy of eigenvectors $x^{(i)}$.
Efficient methods are known for improving...
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Yuxin Ma (Charles University)5/19/26, 11:00 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
The preconditioned conjugate gradient (PCG) algorithm is one of the most popular algorithms for solving large-scale linear systems $Ax = b$, where $A$ is a symmetric positive definite matrix. Rather than computing residuals directly, it updates the residual vectors recursively. Current analyses of the conjugate gradient (CG) algorithm in finite precision typically assume that the norm of the...
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Juan Zhang5/19/26, 11:25 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Our work presents a novel mixed precision formulation of the General Alternating-Direction Implicit (GADI) method, designed to accelerate the solution of large-scale sparse linear systems $Ax=b$. By solving the computationally intensive subsystems in low precision (e.g., Bfloat16 or FP32) and performing residual and solution updates in high precision, the proposed method significantly reduces...
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Mantas Mikaitis (University of Leeds)5/19/26, 11:50 AMApproximate Computing in Numerical Linear AlgebraMinisymposium Talk
Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297–313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors $A$ and $B$ are split into integer slices, the product of these slices is computed exactly, and $AB$ is approximated by accumulating these integer products in floating-point...
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