Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal.  extends this result to vector-valued functions with domain and co-domain of dierent dimensions. This extension requires the knowledge of the rank of the Jacobian function on the whole domain. This leads to the sub-problem of extracting an interval sub-matrix of maximum rank from a given interval matrix. Three dierent techniques leading to approximate solutions of this extraction are proposed and compared.
['Mullier Olivier', 'Eric Goubault', 'Michel Kieffer', 'Sylvie Putot']
I am writing a research paper on a idea General inner approximation of vector-valued functions
[{"from": "human", "value": "I am writing a research paper on a idea General inner approximation of vector-valued functions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  addresses the problem of evaluating a subset of the range of a vector-valued function. It is based on a work by Goldsztejn and Jaulin which provides methods based on interval analysis to address this problem when the dimension of the domain and co-domain of the function are equal.  extends this result to vector-valued functions with domain and co-domain of dierent dimensions. This extension requires the knowledge of the rank of the Jacobian function on the whole domain. This leads to the sub-problem of extracting an interval sub-matrix of maximum rank from a given interval matrix. Three dierent techniques leading to approximate solutions of this extraction are proposed and compared."}]