Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Countless algorithms have been developed for the multiplication of univariate polynomials and multiprecision integers, but all those with sub-quadratic time complexity currently require at least Ω( n ) extra space for the computation. A new routine based on the Karatsuba/Ofman algorithm is presented with the same time complexity of  O ( n  1.59 ) but only  O (log  n ) extra space. A second routine based on the method of Schonhage/Strassen achieves the same pseudo-linear time and  O (1) extra space, but only under certain conditions. A preliminary implementation over  F   p  [χ], where  p  fits into a single machine word, is presented and compared with existing software.
['Daniel S. Roche']
I am writing a research paper on a idea Space- and time-efficient polynomial multiplication
[{"from": "human", "value": "I am writing a research paper on a idea Space- and time-efficient polynomial multiplication"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Countless algorithms have been developed for the multiplication of univariate polynomials and multiprecision integers, but all those with sub-quadratic time complexity currently require at least \u03a9( n ) extra space for the computation. A new routine based on the Karatsuba/Ofman algorithm is presented with the same time complexity of  O ( n  1.59 ) but only  O (log  n ) extra space. A second routine based on the method of Schonhage/Strassen achieves the same pseudo-linear time and  O (1) extra space, but only under certain conditions. A preliminary implementation over  F   p  [\u03c7], where  p  fits into a single machine word, is presented and compared with existing software."}]