Search Results - "HIGHAM, NICHOLAS J."

The Scaling and Squaring Method for the Matrix Exponential Revisited by Higham, Nicholas J.

“…The scaling and squaring method is the most widely used method for computing the matrix exponential, not least because it is the method implemented in the…”
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Stochastic rounding: implementation, error analysis and applications by Croci, Matteo, Fasi, Massimiliano, Higham, Nicholas J, Mary, Theo, Mikaitis, Mantas

“…Stochastic rounding (SR) randomly maps a real number to one of the two nearest values in a finite precision number system. The probability of choosing either…”
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Adaptive precision in block‐Jacobi preconditioning for iterative sparse linear system solvers by Anzt, Hartwig, Dongarra, Jack, Flegar, Goran, Higham, Nicholas J., Quintana‐Ortí, Enrique S.

“…Summary We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block‐Jacobi…”
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A survey of numerical linear algebra methods utilizing mixed-precision arithmetic by Abdelfattah, Ahmad, Anzt, Hartwig, Boman, Erik G, Carson, Erin, Cojean, Terry, Dongarra, Jack, Fox, Alyson, Gates, Mark, Higham, Nicholas J, Li, Xiaoye S, Loe, Jennifer, Luszczek, Piotr, Pranesh, Srikara, Rajamanickam, Siva, Ribizel, Tobias, Smith, Barry F, Swirydowicz, Kasia, Thomas, Stephen, Tomov, Stanimire, Tsai, Yaohung M, Yang, Ulrike Meier

“…The efficient utilization of mixed-precision numerical linear algebra algorithms can offer attractive acceleration to scientific computing applications…”
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Numerical behavior of NVIDIA tensor cores by Fasi, Massimiliano, Higham, Nicholas J, Mikaitis, Mantas, Pranesh, Srikara

“…We explore the floating-point arithmetic implemented in the NVIDIA tensor cores, which are hardware accelerators for mixed-precision matrix multiplication…”
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Performance impact of precision reduction in sparse linear systems solvers by Zounon, Mawussi, Higham, Nicholas J, Lucas, Craig, Tisseur, Françoise

“…It is well established that reduced precision arithmetic can be exploited to accelerate the solution of dense linear systems. Typical examples are mixed…”
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Explicit solutions to correlation matrix completion problems, with an application to risk management and insurance by Georgescu, Dan I., Higham, Nicholas J., Peters, Gareth W.

“…We derive explicit solutions to the problem of completing a partially specified correlation matrix. Our results apply to several block structures for the…”
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Accurately computing the log-sum-exp and softmax functions by Blanchard, Pierre, Higham, Desmond J, Higham, Nicholas J

“…Evaluating the log-sum-exp function or the softmax function is a key step in many modern data science algorithms, notably in inference and classification…”
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Matrix Depot: an extensible test matrix collection for Julia by Zhang, Weijian, Higham, Nicholas J

“…Matrix Depot is a Julia software package that provides easy access to a large and diverse collection of test matrices. Its novelty is threefold. First, it is…”
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Mixed-precision iterative refinement using tensor cores on GPUs to accelerate solution of linear systems by Haidar, Azzam, Bayraktar, Harun, Tomov, Stanimire, Dongarra, Jack, Higham, Nicholas J.

“…Double-precision floating-point arithmetic (FP64) has been the de facto standard for engineering and scientific simulations for several decades. Problem…”
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Numerical algorithms for high-performance computational science by Dongarra, Jack, Grigori, Laura, Higham, Nicholas J

“…A number of features of today's high-performance computers make it challenging to exploit these machines fully for computational science. These include…”
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Solving block low-rank linear systems by LU factorization is numerically stable by Higham, Nicholas J, Mary, Theo

“…Abstract Block low-rank (BLR) matrices possess a blockwise low-rank property that can be exploited to reduce the complexity of numerical linear algebra…”
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Anymatrix: an extensible MATLAB matrix collection by Higham, Nicholas J., Mikaitis, Mantas

“…Anymatrix is a MATLAB toolbox that provides an extensible collection of matrices with the ability to search the collection by matrix properties. Each matrix is…”
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Anderson acceleration of the alternating projections method for computing the nearest correlation matrix by Higham, Nicholas J., Strabić, Nataša

“…In a wide range of applications it is required to compute the nearest correlation matrix in the Frobenius norm to a given symmetric but indefinite matrix. Of…”
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Scaling, sensitivity and stability in the numerical solution of quadratic eigenvalue problems by Higham, Nicholas J., Mackey, D. Steven, Tisseur, Françoise, Garvey, Seamus D.

“…The most common way of solving the quadratic eigenvalue problem (QEP) (λ2 M + λD + K)x = 0 is to convert it into a linear problem (λX + Y)z = 0 of twice the…”
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The Influence and Contribution of Jack Dongarra to Numerical Linear Algebra by Hammarling, Sven, Higham, Nicholas J.

“…This article is dedicated to Jack Dongarra on the occasion of him receiving the 2021 ACM Turing Award and concentrates primarily on his contributions to…”
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Cholesky factorization by Higham, Nicholas J.

“…This article aimed at a general audience of computational scientists, surveys the Cholesky factorization for symmetric positive definite matrices, covering…”
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Integer matrix factorisations, superalgebras and the quadratic form obstruction by Higham, Nicholas J., Lettington, Matthew C., Schmidt, Karl Michael

“…We identify and analyse obstructions to factorisation of integer matrices into products NTN or N2 of matrices with rational or integer entries. The…”
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On pth roots of stochastic matrices by HIGHAM, Nicholas J, LIJING LIN

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An algorithm to compute the polar decomposition of a 3 × 3 matrix by Higham, Nicholas J., Noferini, Vanni

“…We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and…”
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