Improved Computing-Efficiency Least-Squares Algorithm with Application to All-Pass Filter Design

Table 1

Comparison of computational requirements for associated matrices.

Matrix or vector	Operation	Algorithm
		Conventional	Kidambi [13]	Proposed
𝐐	Addition	(3𝐿−1)𝑁^2
	Multiplication	3𝐿𝑁^2
	Sine or cosine	2𝐿𝑁^2
𝐓	Addition		(2𝐿−1)𝑁	3𝑁
	Multiplication		𝐿𝑁	6𝑁
	Sine or cosine		𝐿𝑁	3𝑁
𝐇	Addition		(3𝐿−1)(2𝑁−1)	3(2𝑁−1)
	Multiplication		2𝐿(2𝑁−1)	7(2𝑁−1)
	Sine or cosine		𝐿(2𝑁−1)	3(2𝑁−1)
𝐝	Addition	(2𝐿−1)𝑁	(2𝐿−1)𝑁	3𝑁
	Multiplication	2𝐿𝑁	2𝐿𝑁	5𝑁
	Sine or cosine	2𝐿𝑁	2𝐿𝑁	3𝑁
Total	Addition	3𝐿𝑁^2−𝑁^2+2𝐿𝑁−𝑁	10𝐿𝑁−3𝐿−4𝑁+1	12𝑁−3
	Multiplication	3𝐿𝑁^2+2𝐿𝑁	7𝐿𝑁−3𝐿	25𝑁−7
	Sine or cosine	2𝐿𝑁^2+2𝐿𝑁	5𝐿𝑁−𝐿	12𝑁−3