Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The analysis of algorithms in IEEE floating-point arithmetic is most often carried out via repeated applications of the so-called standard model, which bounds the relative error of each basic operation by a common epsilon depending only on the format. While this approach has been eminently useful for establishing many accuracy and stability results, it fails to capture most of the low-level features that make floating-point arithmetic so highly structured. ,  survey some of those properties and how to exploit them in rounding error analysis. In particular,  review some recent improvements of several classical, Wilkinson-style error bounds from linear algebra and complex arithmetic that all rely on such structure properties.
['Claude-Pierre Jeannerod']
I am writing a research paper on a idea Exploiting Structure in Floating-Point Arithmetic
[{"from": "human", "value": "I am writing a research paper on a idea Exploiting Structure in Floating-Point Arithmetic"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The analysis of algorithms in IEEE floating-point arithmetic is most often carried out via repeated applications of the so-called standard model, which bounds the relative error of each basic operation by a common epsilon depending only on the format. While this approach has been eminently useful for establishing many accuracy and stability results, it fails to capture most of the low-level features that make floating-point arithmetic so highly structured. ,  survey some of those properties and how to exploit them in rounding error analysis. In particular,  review some recent improvements of several classical, Wilkinson-style error bounds from linear algebra and complex arithmetic that all rely on such structure properties."}]