Tridiagonal matrix algorithm

Abstract: In this research, we used Geodesic Active Contour (GAC) model to detect the edges of brain and breast tumor on MRI images. An additive operator splitting (AOS) method is employed in the two dimensional GAC model to maintain the numerical consistency and makes the GAC model computationally efficient. The numerical discretization scheme for GAC model is semi-implicit and unconditional stable lead to sparse system matrix which is a block tridiagonal square matrix. The proposed AOS scheme capable to decompose the sparse system matrix into a strictly diagonally dominant tridiagonal matrix that can be solved very efficiently likes a one dimensional problem. Gauss Seidel and AGE method is used to solve the linear system equations. The AGE employs the fractional splitting strategy which is applied alternately at each half (intermediate) time step on tridiagonal system of difference scheme and it is proved to be stable. This advanced iterative method is extremely powerful, flexible and affords users many advantages. MATLAB has been choosing as the development platform for the implementations and the experiments since it is well suited for the kind of computations required. In the implementation of GAC-AOS model for edges detection of tumor, the experimental results demonstrate that the AGE method gives the best performance compared to Gauss Seidel method in term of time execution, number of iterations,.RMSE, accuracy and computational cost.

Abstract: In this paper, we consider the problem of solving tridiagonal linear systems on distributed-memory multiprocessors. We present a new parallel partition-based tridiagonal solver that is suitable for such parallel computers. As compared with the well representative algorithm-cyclic reduction and its parallel variant-cyclic elimination, our algorithm exploits sufficient high of parallelism throughout without incurring more data traffic.