A Novel Parallel Algorithm Based on the Gram-Schmidt Method for Tridiagonal Linear Systems of Equations

Table 3

The computation time, speed up, and efficiency of parallel solution of the systems of equations with different order.

		Processors no.
		1	2	4	6	10	12	14	16	18
n = 100 000	T	0.00338	0.00175	0.00092	0.00067	0.00056	0.00051	0.00051	0.00052	0.00054
	Sp	—	1.927	3.651	5.027	5.954	6.528	6.566	6.466	6.171
	Ep	—	0.964	0.913	0.838	0.744	0.653	0.547	0.462	0.386
n = 200 000	T	0.02495	0.01289	0.00678	0.00487	0.00406	0.00365	0.00347	0.00336	0.00336
	Sp	—	1.935	3.679	5.121	6.139	6.822	7.180	7.425	7.423
	Ep	—	0.968	0.920	0.854	0.767	0.682	0.598	0.530	0.464
n = 300 000	T	0.05973	0.03025	0.01601	0.01140	0.00931	0.00821	0.00761	0.00700	0.00662
	Sp	—	1.974	3.731	5.239	6.413	7.272	7.845	8.523	9.017
	Ep	—	0.987	0.933	0.873	0.802	0.727	0.654	0.609	0.564
n = 400 000	T	0.12345	0.06221	0.03225	0.02252	0.01787	0.015.441	0.01427	0.01320	0.01236
	Sp	—	1.984	3.828	5.482	6.907	7.995	8.635	9.350	9.983
	Ep	—	0.992	0.957	0.914	0.863	0.800	0.720	0.668	0.624
n = 500 000	T	0.26724	0.12916	0.06842	0.04718	0.03648	0.03094	0.02694	0.02397	0.02248
	Sp	—	2.069	3.905	5.664	7.325	8.635	9.918	11.147	11.887
	Ep	—	1.034	0.976	0.944	0.916	0.864	0.827	0.796	0.743