v1.0.0

Author: armancodv

README.md

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+# TDMA (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
+![Equations](docs/1.svg)
+where ![Equations](docs/2.svg) and ![Equations](docs/3.svg).
+![Equations](docs/4.svg)
+
+## Install
+```
+npm install tdma
+```
+
+## Sample Code
+Using coefficientMatrix
+```
+const tdma = require('tdma');
+
+const coefficientMatrix = [
+    [2, 3, 0, 0],
+    [6, 3, 9, 0],
+    [0, 2, 5, 2],
+    [0, 0, 4, 3]
+];
+const rigthHandSideVector = [21, 69, 34, 22];
+
+const answer = tdma.solver(coefficientMatrix, rigthHandSideVector);
+console.log(answer);
+```
+
+Using Diagonals
+```
+const tdma = require('tdma');
+
+const a = [0, 6, 2, 4];
+const b = [2, 3, 5, 3];
+const c = [3, 9, 2, 0];
+const d = [21, 69, 34, 22];
+
+const answer = tdma.tdma(a, b, c, d);
+console.log(answer);
+```
+
+
+## Method
+The forward sweep consists of modifying the coefficients as follows, denoting the new coefficients with primes:
+![Equations](docs/5.svg)
+and
+![Equations](docs/6.svg)
+The solution is then obtained by back substitution:
+![Equations](docs/7.svg)
+![Equations](docs/8.svg)
+The method above preserves the original coefficient vectors. If this is not required, then a much simpler form of the algorithm is
+![Equations](docs/9.svg)
+followed by the back substitution
+![Equations](docs/10.svg)
+![Equations](docs/11.svg)
+
+Reference: https://en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm