Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Clement or Sylvester–Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations.  consider a new class of appealing two-parameter extensions of this matrix which have the same simple structure and whose eigenvalues are also given explicitly by a simple closed form expression. The aim of this paper is to present in an accessible form these new matrices and examine some numerical results regarding the use of these extensions as test matrices for numerical eigenvalue computations.
['Roy Oste', 'Joris Van der Jeugt']
I am writing a research paper on a idea Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix
[{"from": "human", "value": "I am writing a research paper on a idea Tridiagonal test matrices for eigenvalue computations: two-parameter extensions of the Clement matrix"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The Clement or Sylvester\u2013Kac matrix is a tridiagonal matrix with zero diagonal and simple integer entries. Its spectrum is known explicitly and consists of integers which makes it a useful test matrix for numerical eigenvalue computations.  consider a new class of appealing two-parameter extensions of this matrix which have the same simple structure and whose eigenvalues are also given explicitly by a simple closed form expression. The aim of this paper is to present in an accessible form these new matrices and examine some numerical results regarding the use of these extensions as test matrices for numerical eigenvalue computations."}]