Calculating the basis expansion of a function in CUDA

At Reduce matrix rows with CUDA and Reduce matrix columns with CUDA, different solutions have been described to reduce matrix rows or columns in CUDA. Here, we just want to point out how the approach of reducing the columns of a matrix through the multiplication of a row by the same matrix can be generalized to perform the linear combination of an ensemble of vectors. In other words, if one wants to calculate the following vector basis expansion where f(xm) are samples of the function f(x), ...
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