Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The underlying structure inherent in the classical method of undetermined coefficients, which is used to obtain particular solutions to linear constant coefficient (LCC) difference or differential equations, is investigated. A system of equations of the form B=M/sup -1/ A is obtained, where B and A are vectors whose elements are the coefficients of the terms in the expressions for the input and solutions, respectively, to the LCC equations. The structure of M that arises for both LCC difference and differential equations, as ll as moving-average (FIR) systems, are investigated. It is shown that M is always a lor triangular matrix of order (r-1)*(r+1), where r is the degree of the expressions for the input and solutions. Furthermore, M is characterized by r+1 unique elements, each one defining the diagonal and off-diagonal elements, and is a member of an infinite set of matrices, all of order r+1, which form a group. M can be obtained whenever A and B are given. As a result, if one desires an FIR filter whose output is some linear operation, then the computation of M from A and B imposes a set of necessary and sufficient conditions. >
['Howard Holtz', 'Bonita J. Campbell']
I am writing a research paper on a idea An approach to solving linear constant coefficient difference and differential equations
[{"from": "human", "value": "I am writing a research paper on a idea An approach to solving linear constant coefficient difference and differential equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The underlying structure inherent in the classical method of undetermined coefficients, which is used to obtain particular solutions to linear constant coefficient (LCC) difference or differential equations, is investigated. A system of equations of the form B=M/sup -1/ A is obtained, where B and A are vectors whose elements are the coefficients of the terms in the expressions for the input and solutions, respectively, to the LCC equations. The structure of M that arises for both LCC difference and differential equations, as ll as moving-average (FIR) systems, are investigated. It is shown that M is always a lor triangular matrix of order (r-1)*(r+1), where r is the degree of the expressions for the input and solutions. Furthermore, M is characterized by r+1 unique elements, each one defining the diagonal and off-diagonal elements, and is a member of an infinite set of matrices, all of order r+1, which form a group. M can be obtained whenever A and B are given. As a result, if one desires an FIR filter whose output is some linear operation, then the computation of M from A and B imposes a set of necessary and sufficient conditions. >"}]