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Everything about Bidiagonal matrix
Matrix with two nonzero diagonals.
In mathematics, a bidiagonal matrix is a banded matrix with non-zero entries along the main diagonal and either the diagonal above or the diagonal below. This means there are exactly two non-zero diagonals in the matrix. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Bidiagonal matrixA 5-minute orientation
- Skim a recent paper: An isospectral transformation between Hessenberg–bidiagonal matrix pencils and Hessenberg matrices without using subtractionInfluential work since 2022
- Pick up a classic book: A parallel algorithm synthesis procedure for high-performance computer architecturesThe most-reprinted book on the subject
- Read the landmark paper: Parallel Two-Sided Matrix Reduction to Band Bidiagonal Form on Multicore ArchitecturesCited 16 times
- Go sideways: QR algorithmA closely related topic
- Go sideways: Singular value decompositionA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Parallel Two-Sided Matrix Reduction to Band Bidiagonal Form on Multicore Architectures
Negative integral powers of a bidiagonal matrix
A Bidiagonal Matrix Determines Its Hyperbolic SVD to Varied Relative Accuracy
Bidiagonal factorization of the recurrence matrix for the Hahn multiple orthogonal polynomials
An efficient algorithm for a model with a bidiagonal coefficient matrix
A new subtraction-free formula for lower bounds of the minimal singular value of an upper bidiagonal matrix
Matrix bidiagonal form
Bidiagonal matrix factorisations associated with symmetric multiple orthogonal polynomials and lattice paths
🆕 Influential since 2022
An isospectral transformation between Hessenberg–bidiagonal matrix pencils and Hessenberg matrices without using subtraction
Bidiagonal matrix factorisations related to multiple orthogonal polynomials
Bidiagonal Decompositions and Accurate Computations for the Ballot Table and the Fibonacci Matrix
Algorithm to Construct a Tridiagonal Matrix Factored by Bidiagonal Matrices with Prescribed Eigenvalues and Specified Entries
📚 Books worth reading
A parallel algorithm synthesis procedure for high-performance computer architecturesIan N. Dunn, Gerard G.L. Meyer · 2003
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- QR algorithm In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors…
- Singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix into a rotation, followed by a scaling, followed…
- QR decomposition In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of…
- Hessenberg matrix In linear algebra, a Hessenberg matrix is a special kind of square matrix, one that is "almost" triangular. To be exact, an upper Hessenberg matrix has…
- Numerical linear algebra Numerical linear algebra, sometimes called applied linear algebra, is the study of how matrix operations can be used to create computer algorithms which…
- Matrix decomposition In the mathematical discipline of linear algebra, a matrix decomposition or matrix factorization is a factorization of a matrix into a product of matrices…
- Smith normal form In mathematics, the Smith normal form (sometimes abbreviated SNF) is a normal form that can be defined for any matrix (not necessarily square) with entries…
- Moore–Penrose inverse In mathematics, and in particular linear algebra, the Moore–Penrose inverse A+ of a matrix A, often called the pseudoinverse, is the most widely known…