Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166--1192]. It entails finding the rightmost eigenvalues for a sequence of large matrices, and  demonstrate that these eigenvalue problems can be solved in a robust manner by an unconventional eigenvalue solver.  also develop an algorithm for computing the real stability radius of a real and stable matrix, which utilizes a recently developed technique for detecting the loss of stability in a large dynamical system. Both algorithms are tested on large and sparse matrices.
['Minghao W. Rostami']
I am writing a research paper on a idea NEW ALGORITHMS FOR COMPUTING THE REAL STRUCTURED PSEUDOSPECTRAL ABSCISSA AND THE REAL STABILITY RADIUS OF LARGE AND SPARSE MATRICES
[{"from": "human", "value": "I am writing a research paper on a idea NEW ALGORITHMS FOR COMPUTING THE REAL STRUCTURED PSEUDOSPECTRAL ABSCISSA AND THE REAL STABILITY RADIUS OF LARGE AND SPARSE MATRICES"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166--1192]. It entails finding the rightmost eigenvalues for a sequence of large matrices, and  demonstrate that these eigenvalue problems can be solved in a robust manner by an unconventional eigenvalue solver.  also develop an algorithm for computing the real stability radius of a real and stable matrix, which utilizes a recently developed technique for detecting the loss of stability in a large dynamical system. Both algorithms are tested on large and sparse matrices."}]