Monthly Archives: July 2020

What is the Polar Decomposition?

A polar decomposition of with is a factorization , where has orthonormal columns and is Hermitian positive semidefinite. This decomposition is a generalization of the polar representation of a complex number, where corresponds to and to . When is real, … Continue reading

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What Is a Symmetric Positive Definite Matrix?

A real matrix is symmetric positive definite if it is symmetric ( is equal to its transpose, ) and By making particular choices of in this definition we can derive the inequalities Satisfying these inequalities is not sufficient for positive … Continue reading

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What Is the Growth Factor for Gaussian Elimination?

Gaussian elimination is the process of reducing an matrix to upper triangular form by elementary row operations. It consists of stages, in the th of which multiples of row are added to later rows to eliminate elements below the diagonal … Continue reading

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What Is Stochastic Rounding?

In finite precision arithmetic the result of an elementary arithmetic operation does not generally lie in the underlying number system, , so it must be mapped back into by the process called rounding. The most common choice is round to … Continue reading

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