Tridiagonal matrix algorithm

Abstract: Bspline and Bezier methods are two powerful methods for approximation of data in all branches of engineering problems. With some improvements and modifications they can be applied for interpolation of data. Although literature offers different approaches for the formulation of Bspline, there is a set of independent functions that defines the Bspline equation. The numbers of the coefficients of Bspline equation are equal to the numbers of pair data or control points. The advantage of Bspline method is that, the most of set functions diminishes at some control points. Therefore a simple tridiagonal linear system is obtained. The tridiagonal linear system can be easily solved by Thomas algorithm. Bezier curves can be obtained by drawing the governing parametric equations. The parametric equations are Bernstein polynomials. Bezier curve does not pass through all the data points but passes through end points. It is mainly applied for approximation approaches. By considering some complementary points between original points, the Bezier can be forced to pass through all control points, hence it can be applied for interpolation purposes. The drawn curves by this method are smoother and have less sinuosity forms. For the comparison of the interpolation properties, several problems are solved by these two methods. The results explain that both methods are powerful and robust for interpolation of highly non-uniform set of data. The Bezier model is superior to Bspline with regarding to accuracy, smoothness and less calculation operations.

Abstract: A method and algorithm to determine if a tridiagonal Toeplitz matrix is well-condition or weakly well-condition is presented