Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Fast algorithms for matrix multiplication, namely those that perform asymptotically fer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. Hover, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly aker than the classical algorithm, they are not used even in cases where they provide a performance benefit.  argue in this paper that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and  explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and  co...
['Grey Ballard', 'Austin R. Benson', 'Alex Druinsky', 'Benjamin Lipshitz', 'Oded Schwartz']
I am writing a research paper on a idea Improving the numerical stability of fast matrix multiplication
[{"from": "human", "value": "I am writing a research paper on a idea Improving the numerical stability of fast matrix multiplication"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Fast algorithms for matrix multiplication, namely those that perform asymptotically fer scalar operations than the classical algorithm, have been considered primarily of theoretical interest. Apart from Strassen's original algorithm, few fast algorithms have been efficiently implemented or used in practical applications. Hover, there exist many practical alternatives to Strassen's algorithm with varying performance and numerical properties. Fast algorithms are known to be numerically stable, but because their error bounds are slightly aker than the classical algorithm, they are not used even in cases where they provide a performance benefit.  argue in this paper that the numerical sacrifice of fast algorithms, particularly for the typical use cases of practical algorithms, is not prohibitive, and  explore ways to improve the accuracy both theoretically and empirically. The numerical accuracy of fast matrix multiplication depends on properties of the algorithm and of the input matrices, and  co..."}]