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Theory and Modern Applications

Table 3 Rational IFS parameters for monotonic fractal interpolants

From: Rational iterated function system for positive/monotonic shape preservation

Figure

Scaling factors

Shape parameters

3(a)

ξ 6 =0.034, ξ 7 =0.44, ξ 8 =0.789, ξ 9 =0.578, ξ 10 =0.999

α i = β i =1, i = 6(1)10, γ 6 =4.2927, γ 7 =503.3320, γ 8 =1.5805, γ 9 =20.5370, γ 10 =2.4994

3(b)

ξ 6 =0.034, ξ 7 =0.1, ξ 8 =0.789, ξ 9 =0.578, ξ 10 =0.999

α i = β i =1, i = 6(1)10, γ 6 =4.2927, γ 7 =14.3808, γ 8 =1.5805, γ 9 =20.5370, γ 10 =2.4994

3(c)

ξ 6 =0.034, ξ 7 =0.44, ξ 8 =0.789, ξ 9 =0.1, ξ 10 =0.999

α i = β i =1, i = 6(1)10, γ 6 =4.2927, γ 7 =503.3320, γ 8 =1.5805, γ 9 =9.6296, γ 10 =2.4994

3(d)

ξ 6 =0.034, ξ 7 =0.1, ξ 8 =0.1, ξ 9 =0.1, ξ 10 =0.1

α i = β i =1, i = 6(1)10, γ 6 =4.2927, γ 7 =14.3808, γ 8 =1.4227, γ 9 =20.537, γ 10 =2.0408

3(e)

ξ 6 =0.034, ξ 7 =0.44, ξ 8 =0.789, ξ 9 =0.578, ξ 10 =0.999

α i = β i =1, i∈{6,7,8,10}, α 9 = 10 4 , β 9 =10, α 10 =1, β 10 =1, γ 6 =4.2927, γ 7 =503.3320, γ 8 =1.5805, γ 9 =1.1857, γ 10 =2.4994

3(f)

ξ 6 =0.034, ξ 7 =0.1, ξ 8 =0.789, ξ 9 =0.578, ξ 10 =0.999

α i = β i =1, i∈{6,8,9,10}, α 7 = 10 4 , β 7 =10, γ 6 =4.2927, γ 7 =6.3276, γ 8 =1.5805, γ 9 =20.5370, γ 10 =2.4994

3(g)

ξ 6 =0.034, ξ 7 =0.44, ξ 8 =0.789, ξ 9 =0.1, ξ 10 =0.999

α i = β i =1, i∈{6,7,8,10}, α 9 = 10 4 , β 9 =1, γ 6 =4.2927, γ 7 =503.3320, γ 8 =1.5805, γ 9 =5.556, γ 10 =2.4994

3(h)

ξ 6 =0.034, ξ 7 =0.44, ξ 8 =0.789, ξ 9 =0.1, ξ 10 =0.999

α i = β i =1, i∈{6,7,8,10}, α 9 =1, β 9 = 10 4 , γ 6 =4.2927, γ 7 =503.3320, γ 8 =1.5805, γ 9 =4.0796, γ 10 =2.4994

3(i)

ξ i =0, i = 6(1)10

α i = β i =1, i∈{6,7,8,10}, α 9 = 10 4 , β 9 =1, γ 6 =0.0003, γ 7 =0.0011, γ 8 =0.0001, γ 9 =5.0004, γ 10 =0.0002