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Computability in linear algebra

Many problems in Linear Algebra can be solved by Gaussian Elimination. This famous algorithm applies to an algebraic model of real number computation …

Many problems in Linear Algebra can be solved by Gaussian Elimination. This famous algorithm applies to an algebraic model of real number computation where operations + ,-, * ,/ and tests like, e.g., < and == are presumed exact. Implementations of algebraic algorithms on actual digital computers often lead to numerical instabilities, thus revealing a serious discrepancy between model and reality.

A different model of real number computation dating back to Alan Turing considers real numbers as limits of rational approximations.…

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