Table 3 Numerical results for \(\pmb{\mathbb{B}^{+}=[1,2; 2,5]}\) , \(\pmb{\mathbb{B}^{-}=[10,20; 20,50]}\)

Nonsymmetric PIFE (ε = 1)

8 × 8

1.2388E − 1

-

2.3454

-

16 × 16

3.1375E − 2

1.9812

1.1815

0.9892

32 × 32

7.9027E − 3

1.9892

5.9497E − 1

0.9898

64 × 64

1.9817E − 3

1.9956

2.9851E − 1

0.9950

128 × 128

4.9509E − 4

2.0010

1.4946E − 1

0.9980

256 × 256

1.2382E − 4

1.9994

7.4772E − 2

0.9992

Incomplete PIFE (ε = 0)

8 × 8

1.2234E − 1

-

2.3267

-

16 × 16

3.1249E − 2

1.9690

1.1786

0.9812

32 × 32

7.8952E − 3

1.9848

5.9442E − 1

0.9875

64 × 64

1.9834E − 3

1.9930

2.9841E − 1

0.9942

128 × 128

4.9591E − 4

1.9998

1.4941E − 1

0.9980

256 × 256

1.2407E − 4

1.9989

7.4762E − 2

0.9989

Symmetric PIFE (ε = −1)

8 × 8

1.2175E − 1

-

2.3184

-

16 × 16

3.1205E − 2

1.9640

1.1778

0.9771

32 × 32

7.8917E − 3

1.9834

5.9433E − 1

0.9867

64 × 64

1.9836E − 3

1.9923

2.9840E − 1

0.9940

128 × 128

4.9598E − 4

1.9997

1.4939E − 1

0.9981

256 × 256

1.2411E − 4

1.9986

7.4760E − 2

0.9988