On the number of segments needed in a piecewise linear approximation |
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Authors: | C.L. Frenzen |
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Affiliation: | a Department of Applied Mathematics, Naval Postgraduate School, Monterey, CA, 93943-5216, USA b Department of Computer Science and Electronics, Kyushu Institute of Technology, Iizuka, 820-8502, Japan c Department of Electrical and Computer Engineering, Naval Postgraduate School, Monterey, CA, 93943-5121, USA |
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Abstract: | The introduction of high-speed circuits to realize an arithmetic function f as a piecewise linear approximation has created a need to understand how the number of segments depends on the interval a≤x≤b and the desired approximation error ε. For the case of optimum non-uniform segments, we show that the number of segments is given as , (ε→0+), where . Experimental data shows that this approximation is close to the exact number of segments for a set of 14 benchmark functions. We also show that, if the segments have the same width (to reduce circuit complexity), then the number of segments is given by , (ε→0+), where . |
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Keywords: | Piecewise linear approximation Numeric function generators |
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