Low-precision computation is often used to lower the time and energy cost of machine learning, and recently hardware accelerators have been developed to support it. Still, it has been used primarily for inference—not training. Previous low-precision training algorithms suffered from a fundamental tradeoff: as the number of bits of precision is lowered, quantization noise is added to the model, ...

We propose a new method that always fits an ellipse to a point sequence extracted from images. The currently known best ellipse fitting method is hyper-renormalization of Kanatani et al., but it may return a hyperbola when the noise in the data is very large. Our proposed method returns an ellipse close to the point sequence by random sampling of data points. Doing simulation, we show that our ...

We derive a class of extended one-step methods of order m for solving delay-differential equations. This class includes methods of fourth and fifth order of accuracy. Also, the class of these methods depends on two free parameters. A convergence theorem and convergence factor of these methods are given. In addition, we investigate the stability properties of these methods. The results of the ar...

Abstract Bidiagonal factorizations for the change of basis matrices between monomial and Newton polynomial bases are obtained. The total positivity these is characterized in terms sign nodes bases. It shown that computations to high relative accuracy algebraic problems related can be achieved whenever have same sign. Stirling considered particular cases matrices, then collocation Wronskian Touc...