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. Author manuscript; available in PMC: 2013 Mar 1.
Published in final edited form as: Psychol Methods. 2011 Nov 21;17(1):61–77. doi: 10.1037/a0025814

Table 1.

Accuracy of Using Truncated Power Splines to Approximate Three Functions

Functions being approximated
K exp(2t − 1) 8t(1 − t) sin2(2πt)
0 0.0450 0.0000 1.0003
1 0.0121 0.0000 1.0057
2 0.0038 0.0000 0.4993
3 0.0018 0.0000 0.6125
4 0.0010 0.0000 0.1828
5 0.0006 0.0000 0.1438
6 0.0004 0.0000 0.0735
7 0.0002 0.0000 0.0413
8 0.0002 0.0000 0.0281
9 0.0001 0.0000 0.0204
10 0.0001 0.0000 0.0146

Note. K is the number of knots of the truncated power splines used to approximate the three functions. K = 0 implies that quadratic functions are used to approximate these functions. Numbers under each function are the “minimal” maximum absolute difference between this function and any truncated power splines with given number of knots (0–10).