Computational mathematics

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Complexity of Matrix Multiplication

Volker Strassen showed that $n^3$ matrix multiplication was not optimal in 1969. Since then, new algorithms such as Coppersmith-Winograd have further improved the time complexity of matrix multiplication. It is conjectured that matrix multiplication is possible in $O(n^{2+ɛ})$ for any $ɛ>0$, however small. This is one of the few remaining open problems in finite-dimensional linear algebra.

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algebra algorithm computational mathematics computer science group theory linear algebra open problem

Gillespie Algorithm

The Gillespie Algorithm for stochastic equations is used heavily in a number of fields of applied mathematics, in particular computational systems biology.

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algorithm applied mathematics biology computational biology computational mathematics computer science differential equation probability stochastic equation

IEEE 754-2008: Floating Point Arithmetic

Most programming languages provide a floating-point type. What is floating point, and how does it work? What caveats should programmers be aware of?

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Tech Talks computational mathematics computer science first year friendly floating point number

Sparse Matrices

Sparse matrices are frequently used in scientific and numerical computation. How do they work? What new findings have there been? Speakers are encouraged to specialize this broad topic to a particular subfield of interest.

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algebra computational mathematics computer science linear algebra