A Family of Modified Even Order Bernoulli-Type Multiquadric Quasi-Interpolants with Any Degree Polynomial Reproduction Property

Table 1

Numerical results of the operators 𝑆_𝐵𝑚 and ℒ_𝑣𝑚 for the saddle function.

𝑆𝐵𝑚𝑓1			ℒ𝑣𝑚𝑓1
(𝜇,𝑚)	𝜀mean	𝜀max	(𝑙,𝑚)	𝜀mean	𝜀max
(2,1)	1.002×10^−3	4.786×10^−3	(2,1)	2.237×10^−4	1.126×10^−3
(2,2)	5.836×10^−4	3.654×10^−3	(2,2)	3.356×10^−6	2.745×10^−5
(2,3)	4.148×10^−4	2.776×10^−3	(2,3)	4.020×10^−7	2.300×10^−6
(3,1)	4.100×10^−4	2.578×10^−3	(3,1)	2.063×10^−4	1.097×10^−3
(3,2)	1.626×10^−4	1.200×10^−3	(3,2)	1.698×10^−6	2.623×10^−5
(3,3)	6.893×10^−5	2.332×10^−4	(3,3)	1.325×10^−8	2.021×10^−7
(4,1)	3.008×10^−4	3.643×10^−3	(4,1)	1.824×10^−4	1.053×10^−3
(4,2)	1.822×10^−4	2.004×10^−4	(4,2)	9.620×10^−7	2.363×10^−5
(4,3)	1.844×10^−5	5.491×10^−4	(4,3)	9.891×10^−8	2.031×10^−7