Tridiagonal matrix algorithm
In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and .
- Comment
- enIn numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and .
- Has abstract
- enIn numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as where and . For such systems, the solution can be obtained in operations instead of required by Gaussian elimination. A first sweep eliminates the 's, and then an (abbreviated) backward substitution produces the solution. Examples of such matrices commonly arise from the discretization of 1D Poisson equation and natural cubic spline interpolation. Thomas' algorithm is not stable in general, but is so in several special cases, such as when the matrix is diagonally dominant (either by rows or columns) or symmetric positive definite; for a more precise characterization of stability of Thomas' algorithm, see Higham Theorem 9.12. If stability is required in the general case, Gaussian elimination with partial pivoting (GEPP) is recommended instead.
- Is primary topic of
- Tridiagonal matrix algorithm
- Label
- enTridiagonal matrix algorithm
- Link from a Wikipage to an external page
- archive.org/details/elementarynumeri00samu
- apps.nrbook.com/empanel/index.html%3Fpg=56
- Link from a Wikipage to another Wikipage
- Block matrix
- Category:Articles with example BASIC code
- Category:Numerical linear algebra
- Dev-C++
- Diagonally dominant
- Gaussian elimination
- Llewellyn Thomas
- Numerical linear algebra
- Numerical stability
- Partial pivoting
- Periodic boundary conditions
- Poisson equation
- Poisson equation discretized into block tridiagonal
- Sherman–Morrison formula
- Spline interpolation
- Symmetric positive definite
- Tridiagonal matrix
- Visual Basic for Applications
- SameAs
- Algoritmo de Thomas
- Algoritmo di soluzione dei sistemi tridiagonali
- Algoritmo para matrices tridiagonales
- m.0bgfg3
- mEnQ
- Q1819156
- Thomas-Algorithmus
- Tridiagonale-matrix-algoritme
- Tridiagonal matris algoritması
- Метод прогонки
- Метод прогонки
- त्रिविकर्णिक आव्यूह कलनविधि
- 三对角矩阵算法
- Subject
- Category:Articles with example BASIC code
- Category:Numerical linear algebra
- WasDerivedFrom
- Tridiagonal matrix algorithm?oldid=1117006478&ns=0
- WikiPageLength
- 17625
- Wikipage page ID
- 4068264
- Wikipage revision ID
- 1117006478
- WikiPageUsesTemplate
- Template:CFDWiki
- Template:Cite book
- Template:Numerical linear algebra
- Template:Short description
- Template:Wikibooks