Combined Preorder and Postorder Traversal Algorithm for the Analysis of Singular Systems by Haar Wavelets

Table 1

Flop counts for various sizes of the matrix A and resolution scales.

𝐽	𝐀∈𝑅^4×4				𝐀∈𝑅^20×20
	Kronecker	Proposed algorithm			Kronecker	Proposed algorithm
	method	WinSolver	WinTree	Total	method	WinSolver	WinTree	Total
2	4096	160	0	160	512000	16800	0	16800
5	2097152	1280	3360	4640	262144000	134400	32160	166560
10	6.871×10^10	40960	89534464	89575424	8.589×10^12	4300800	448983040	453283840
12	4.398×10^12	163840	5.726×10^9	5.727×10^9	5.497×10^14	17203200	2.864×10^10	2.867×10^10
15	2.251×10^15	1310720	2.932×10^12	2.932×10^12	2.814×10^17	137625600	1.466×10^13	1.466×10^13
18	1.152×10^18	10485760	1.501×10^15	1.501×10^15	1.441×10^20	1101004800	7.506×10^15	7.506×10^15
20	7.378×10^19	83886080	4.194×10^16	4.194×10^16	9.223×10^21	4.404×10^9	4.803×10^17	4.803×10^17