Schrödinger’s tridiagonal matrix
نویسندگان
چکیده
منابع مشابه
A Tridiagonal Matrix
= αI +βT, where T is defined by the preceding formula. This matrix arises in many applications, such as n coupled harmonic oscillators and solving the Laplace equation numerically. Clearly M and T have the same eigenvectors and their respective eigenvalues are related by μ = α+βλ . Thus, to understand M it is sufficient to work with the simpler matrix T . Eigenvalues and Eigenvectors of T Usu...
متن کاملA Tridiagonal Approach to Matrix Integrals
Physicists in the 70’s starting with ’t Hooft established that the number of suitably labeled planar maps with prescribed vertex degree distribution can be represented as the leading coefficient of the 1 N -expansion of a joint cumulant of traces of powers of a standard N-by-N GUE matrix. Here we undertake the calculation of this leading coefficient in a different way, namely, after first tridi...
متن کاملOn an Inverse Formula of a Tridiagonal Matrix
This paper provides an inverse formula freed of determinant expressions for a general tridiagonal matrix. This is viewed as an alternative version of the Usmani formula, which easily tends to blow up computationally. We discuss a number of different viewpoints regarding the proposed and Usmani’s formulas, such as the proof method and the meaning of included terms, although our formula itself ma...
متن کاملAccurate polynomial root-finding methods for symmetric tridiagonal matrix eigenproblems
In this paper we consider the application of polynomial root-finding methods to the solution of the tridiagonal matrix eigenproblem. All considered solvers are based on evaluating the Newton correction. We show that the use of scaled three-term recurrence relations complemented with error free transformations yields some compensated schemes which significantly improve the accuracy of computed r...
متن کاملEfficient tridiagonal preconditioner for the matrix-free truncated Newton method
In this paper, we study an efficient tridiagonal preconditioner, based on numerical differentiation, applied to the matrix-free truncated Newton method for unconstrained optimization. It is proved that this preconditioner is positive definite for many practical problems. The efficiency of the resulting matrix-free truncated Newton method is demonstrated by results of extensive numerical experim...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Special Matrices
سال: 2021
ISSN: 2300-7451
DOI: 10.1515/spma-2020-0124