and obtain an approximation by truncating to be less than some threshold (which, in practice, would be a small power of ): Thus, for instance, if , the approximant would be taken to be One could also use the slightly smoother approximation in which case we would take The function is...
This is only optimal in the regime ; we expect to establish some eigenvalue repulsion, improving the RHS to for real matrices and for complex matrices, but this appears to be a more difficult task (possibly requiring some quadratic inverse Littlewood-Offord theory, rather than just linear ...
What's New in TextPipe v10.7.2 - July 17, 2018 Fixed @inputFile@ truncating last character of filename. Updated main memo control to fix intermittent stack overflow issue. What's New in TextPipe v10.7.1 - May 25, 2018 Workaround for Trial Output area not always showing result dat...
So, an obvious need for dither is when you reduce a 16-bit sound file to eight bits. Instead of truncating or rounding to fit the samples into the reduced word size—creating harmonic and intermodulation distortion—the added dither spreads the error out over time, as broadband noise. But ...