TY - JOUR T1 - Numerical Stability in Complex Summation TT - پایداری عددی در مجموع‌یابی مختلط JF - khu-mmr JO - khu-mmr VL - 7 IS - 2 UR - http://mmr.khu.ac.ir/article-1-2859-en.html Y1 - 2021 SP - 389 EP - 396 KW - complex summation KW - condition number KW - numerical stability KW - cancellation. N2 - The natural and practical condition numbers for summation of complex numbers are introduced. These numbers measure the effect of loss of significant digits on the round-off error when computing a sum in floating point arithmetic. The relationship between the natural and practical condition numbers and their size are studied. It is shown that the practical condition number is equal to one when all the summands lie in one of the quadrants of the complex plane. Also, an upper bound for the natural condition number is obtained when the summands lie in a sector with an angle less than or equal to pi/2../files/site1/files/72/16Abstract.pdf M3 10.52547/mmr.7.2.389 ER -