Table 8. Comparison of proposed model with sequential multiplication.

No. of matrix	Sequence of dimensions	Optimal parenthesis	Sequential multiplication	GCO multiplication	Improvement
9	94,67,56,17,80,68,10,78,7,5	(M1*(M2*(M3*(M4*(M5*(M6*((M7*M8)*M9)))))))	1,273,230	98,220	92%
12	42,54,49,22,62,46,93,97,82,59,24,86,56	(((M1*(M2*M3))*((((((M4*M5)*M6)*M7)*M8)*M9)*M10))*(M11*M12))	1,777,734	970,214	45%
15	27,98,89,40,36,82,6,11,3,23,15,91,87,35,3,43	((M1*(M2*(M3*(M4*(M5*(M6*((M7*M8)*((M9*M10)*(M11*(M12*(M13*M14)))))))))))*M15)	816,480	101,322	88%
18	94,30,63,79,52,10,6,13,93,97,3,8,67,40,38,6,89,61,71	((M1*(M2*(M3*(M4*(M5*(M6*(M7*(M8*(M9*M10)))))))))*(((((((M11*M12)*M13)*M14)*M15)*M16)*M17)*M18))	3,518,984	139,845	96%
21	57,92,76,77,28,13,47,27,3,67,89,4,93,16,24,4,14,83,89,92,33,19	((M1*(M2*(M3*(M4*(M5*(M6*(M7*M8)))))))*((((((((((((M9*M10)*M11)*M12)*M13)*M14)*M15)*M16)*M17)*M18)*M19)*M20)*M21))	2,658,537	158,058	94%
24	79,68,62,22,98,35,62,99,21,39,91,79,81,31,11,4,87,90,90,72,57,92,3 6,72,59	((M1*(M2*(M3*(M4*(M5*(M6*(M7*(M8*(M9*(M10*(M11*(M12*(M13*(M14*M15))))))))))))))*((((((((M16*M17)*M18)*M19)*M20)*M21)*M22)*M23)*M24))	6,688,377	377,216	95%
30	50,44,56,33,44,5,9,10,12,22,32,26,41,28,19,29,41,23,18,25,22,34,33,13,33,11,43,21,24,56,71	((M1*(M2*(M3*(M4*M5))))*((((((((((((((((((((((((M6*M7)*M8)*M9)*M10)*M11)*M12)*M13)*M14)*M15)*M16)*M17)*M18)*M19)*M20)*M21)*M22)*M23)*M24)*M25)*M26)*M27)*M28)*M29)*M30))	1,258,650	153,290	88%
50	56,34,33,46,39,50,65,32,10,15,30,24,25,13,7,11,19,30,15,3,20,31,50,9,10,16,44,22,10,16,44,22,10,19,30,40,45,23,22,14,30,11,22,24,32,15,19,29,34,5,9,23,29,34,9	((M1*(M2*(M3*(M4*(M5*(M6*(M7*(M8*(M9*(M10*(M11*(M12*(M13*(M14*(M15*(M16*(M17*(M18*M19))))))))))))))))))*((((((((((((((((((((((((((((((((((M20*M21)*M22)*M23)*M24)*M25)*M26)*M27)*M28)*M29)*M30)*M31)*M32)*M33)*M34)*M35)*M36)*M37)*M38)*M39)*M40)*M41)*M42)*M43)*M44)*M45)*M46)*M47)*M48)*M49)*M50)*M51)*M52)*M53)*M54))	1,969,800	112,434	93%