Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an extended Lanczos bidiagonalization algorithm for finding a low rank approximation of a given matrix.  show that this method can yield better low-rank approximations than standard Lanczos bidiagonalization algorithm, without increasing the cost too much.  also describe a partial reorthogonalization process that can be used to maintain an adequate level of orthogonality of the Lanczos vectors in order to produce accurate low-rank approximations.  demonstrate the effectiveness and applicability of our algorithm for a number of applications.
['Xuansheng Wang', 'François Glineur', 'Linzhang Lu', 'Paul Van Dooren']
I am writing a research paper on a idea Extended Lanczos bidiagonalization algorithm for low rank approximation and its applications
[{"from": "human", "value": "I am writing a research paper on a idea Extended Lanczos bidiagonalization algorithm for low rank approximation and its applications"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose an extended Lanczos bidiagonalization algorithm for finding a low rank approximation of a given matrix.  show that this method can yield better low-rank approximations than standard Lanczos bidiagonalization algorithm, without increasing the cost too much.  also describe a partial reorthogonalization process that can be used to maintain an adequate level of orthogonality of the Lanczos vectors in order to produce accurate low-rank approximations.  demonstrate the effectiveness and applicability of our algorithm for a number of applications."}]