Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an algorithm for solving a linear system in a symmetric M-matrix.#R##N#In particular, for $n times n$ symmetric M-matrix $M$,  show how to find a diagonal matrix $D$ such that#R##N#$DMD$ is diagonally-dominant. To compute $D$, the algorithm must solve $O{log n}$ linear systems in diagonally-dominant matrices. If  solve these diagonally-dominant systems approximately using the Spielman-Teng#R##N#nearly-linear time solver, then  obtain an algorithm for approximately solving linear systems in symmetric M-matrices, for which the expected running time is also nearly-linear.
['Samuel I. Daitch', 'Daniel A. Spielman']
I am writing a research paper on a idea A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix ?
[{"from": "human", "value": "I am writing a research paper on a idea A Nearly-Linear Time Algorithm for Approximately Solving Linear Systems in a Symmetric M-Matrix ?"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an algorithm for solving a linear system in a symmetric M-matrix.#R##N#In particular, for $n times n$ symmetric M-matrix $M$,  show how to find a diagonal matrix $D$ such that#R##N#$DMD$ is diagonally-dominant. To compute $D$, the algorithm must solve $O{log n}$ linear systems in diagonally-dominant matrices. If  solve these diagonally-dominant systems approximately using the Spielman-Teng#R##N#nearly-linear time solver, then  obtain an algorithm for approximately solving linear systems in symmetric M-matrices, for which the expected running time is also nearly-linear."}]