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Everything about Tridiagonal matrix
Matrix with nonzero elements on the main diagonal and the diagonals above and below it
In linear algebra, a tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the subdiagonal/lower diagonal, and the supradiagonal/upper diagonal. For example, the following matrix is tridiagonal: Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Tridiagonal matrixA 5-minute orientation
- Skim a recent paper: On a class of non-Hermitian Hamiltonians with tridiagonal matrix representationInfluential work since 2022
- Pick up a classic book: Introduction to numerical analysis and scientific computingThe most-reprinted book on the subject
- Read the landmark paper: Inversion of a tridiagonal jacobi matrixCited 143 times
- Go sideways: Eigenvalue algorithmA closely related topic
- Go sideways: Toeplitz matrixA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Inversion of a tridiagonal jacobi matrix
The inverse of a tridiagonal matrix
Algorithm for solving tridiagonal matrix problems in parallel
Inversion of Jacobi's tridiagonal matrix
Explicit inverse of a tridiagonal k−Toeplitz matrix
The eigenproblem of a tridiagonal 2-Toeplitz matrix
On the inverse of a general tridiagonal matrix
Matrix Measures and Random Walks with a Block Tridiagonal Transition Matrix
🆕 Influential since 2022
On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation
Tridiagonal matrix decomposition for Hamiltonian simulation on a quantum computer
A division-free algorithm for numerically evaluating the determinant of a specific quasi-tridiagonal matrix
Complex tridiagonal quantum Hamiltonians and matrix continued fractions
Parallel tridiagonal matrix inversion with a hybrid multigrid-Thomas algorithm method
📚 Books worth reading
Introduction to numerical analysis and scientific computingNabil Nassif · 2014
Data structures, algorithms, and applications in C++Sartaj Sahni · 1998
An accelerated bisection method for the calculation of eigenvalues of a symmetric tridiagonal matrixHerbert J. Bernstein · 1983- 📕Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputersRichard A. Blech · 1989
- 📕Parallel Gaussian estimation of a block tridiagonal matrix using multiple microcomputersRichard A. Blech · 1989
- 📕Parallel Gaussian elimination of a block tridiagonal matrix using multiple microcomputersRichard A. Blech · 1989
- 📕Parallel Gaussian Elimination of a Block Tridiagonal Matrix Using Multiple Microcomputers · 2018
- 📕Two working algorithms for the eigenvalues of a symmetric tridiagonal matrixW. Kahan · 1966
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Hermitian matrix In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose…
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