Classifier Instance:

Anchor text: Volker Strassen
Target Entity: Volker_Strassen
Preceding Context: The running time of square matrix multiplication, if carried out naïvely, is O( n^3 ) . The running time for multiplying rectangular matrices (one m×p-matrix with one p×n-matrix) is O(mnp), however, more efficient algorithms exist, such as Strassen's algorithm, devised by
Succeeding Context: in 1969 and often referred to as "fast matrix multiplication". It is based on a way of multiplying two 2×2-matrices which requires only 7 multiplications (instead of the usual 8), at the expense of several additional addition and subtraction operations. Applying this recursively gives an algorithm with a multiplicative cost of O( n^{\log_{2}7}) \approx O(n^{2.807}) . Strassen's algorithm is more complex compared to the naïve algorithm, and it lacks numerical stability. Nevertheless, it appears in several libraries, such as BLAS, where it is significantly more efficient for matrices with dimensions n > 100, and is very useful for large matrices over exact domains such as finite fields, where numerical stability is not an issue.
Paragraph Title: Algorithms for efficient matrix multiplication
Source Page: Matrix multiplication

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