TY - JOUR

T1 - Extended use of error-free transformation for real matrix multiplication to complex matrix multiplication

AU - Kazal, Nurul Yakim

AU - Mukhlash, Imam

AU - Sanjoyo, Bandung Arry

AU - Hidayat, Nurul

AU - Ozaki, Katsuhisa

N1 - Publisher Copyright:
© Published under licence by IOP Publishing Ltd.

PY - 2021/3/29

Y1 - 2021/3/29

N2 - The presence of rounding errors is frequently inevitable when performing arithmetic operations in computers due to the use of floating-point number system whose elements have finite precision. Consequently, error-free transformation algorithms are proposed as solutions, and a particular instance of these is the error-free transformation algorithm for real matrix multiplication. Based on the previously mentioned algorithm, this study proposes two error-error free transformation algorithms for complex matrix multiplication. By conducting the numerical experiment, one finds that the combination of both proposed algorithms with an accurate summation algorithm generates the most accurate results, but it also suffers from a notable increase in the computing time ratio. On the other hand, the second proposed algorithm, which is simply another form of the first one with the change of order in summation, combined with the pure floating-point addition produces results that are nearly as accurate as those generated by the former combination. Since these results are achieved with significantly smaller computing time ratio, then the study concludes that the last combination is the best method for complex matrix multiplication in terms of accuracy and computing time efficiency.

AB - The presence of rounding errors is frequently inevitable when performing arithmetic operations in computers due to the use of floating-point number system whose elements have finite precision. Consequently, error-free transformation algorithms are proposed as solutions, and a particular instance of these is the error-free transformation algorithm for real matrix multiplication. Based on the previously mentioned algorithm, this study proposes two error-error free transformation algorithms for complex matrix multiplication. By conducting the numerical experiment, one finds that the combination of both proposed algorithms with an accurate summation algorithm generates the most accurate results, but it also suffers from a notable increase in the computing time ratio. On the other hand, the second proposed algorithm, which is simply another form of the first one with the change of order in summation, combined with the pure floating-point addition produces results that are nearly as accurate as those generated by the former combination. Since these results are achieved with significantly smaller computing time ratio, then the study concludes that the last combination is the best method for complex matrix multiplication in terms of accuracy and computing time efficiency.

UR - http://www.scopus.com/inward/record.url?scp=85103910720&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/1821/1/012022

DO - 10.1088/1742-6596/1821/1/012022

M3 - Conference article

AN - SCOPUS:85103910720

SN - 1742-6588

VL - 1821

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

IS - 1

M1 - 012022

T2 - 6th International Conference on Mathematics: Pure, Applied and Computation, ICOMPAC 2020

Y2 - 24 October 2020

ER -