Quantum algorithm for matrix logarithm by integral formula

Wang, Yatian; Xiang, Hua; Zhang, Songling

doi:10.1007/s11128-022-03824-y

Cited by 1 publication

(1 citation statement)

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“…The applicability of the matrix logarithm in so many distinct areas has encouraged the development of different approaches to its evaluation. The traditionally proposed methods incorporate algorithms based on the inverse scaling and squaring technique [27], the Schur-Fréchet procedure [28], the Padé approximants [29][30][31][32][33][34][35][36], arithmetic-geometric mean iteration [37], numerical spectral and Jordan decomposition [38], contour integrals [39], or different quadrature formulas [40][41][42][43]. MATLAB incorporates logm as a built-in function that uses the algorithms described in [33,34] to compute the principal matrix logarithm.…”

Section: Introductionmentioning

confidence: 99%

Computing the Matrix Logarithm with the Romberg Integration Method

Ibáñez,

Alonso,

Defez

et al. 2023

Algorithms

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The matrix logarithm function has applicability in many engineering and science fields. Improvements in its calculation, from the point of view of both accuracy and/or execution time, have a direct impact on these disciplines. This paper describes a new numerical algorithm devoted to matrix logarithm computation and using the Romberg integration method, together with the inverse scaling and squaring technique. This novel method was implemented and compared with three different state-of-the-art codes, all based on Padé approximation. The experimental results, under a heterogeneous matrix test battery, showed that the new method was numerically stable, with an elapsed time midway among the other codes, and it generally offered a higher accuracy.

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