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The point of learning how to write "the QR iteration algorithm" is not because eig will be slower. It is because "the QR iteration algorithm" is easy. When you learn things, you are given easy tasks. We don't teach children how to add 1+1 because we need the answer. We don't teach them how to manually carry on paper when they add 7+17 ...


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In some special cases it may be if you have a special case application that's very different for where the libraries are intended. I have written an optimization application that needs to do 80 million very simple linear programming solutions per second on 8 cores. That's 10 million per second per core. I tested a number of available linear programming ...


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This might be tangent but i feel it worth adding. A common way for user code to beat libraries is to exploit structure the libraries are not aware of. Block diagonal matrices are easier to work in structured form then dense matrix that contain the complete matrix and lots of zeros. Cyclic boundary conditions in PDEs can be solved more easily than working on ...


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