The inverse of a tridiagonal matrix
نویسندگان
چکیده
منابع مشابه
On 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...
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= 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...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2001
ISSN: 0024-3795
DOI: 10.1016/s0024-3795(00)00262-7