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Summary form only given. QR methods for solving Toeplitz tridiagonal systems are well developed with applications in numerous interdisciplinary fields. There is a strong motivation to develop faster, more efficient and, more importantly, scalable algorithms to factor such systems due to their significance in many scientific applications. We present two parallel QR factorization algorithms used to solve Toeplitz tridiagonal systems. QR factorization is accomplished using Householder reflections and Givens rotations. These parallel algorithms exhibit high scalability and near linear to superlinear speedup on large system sizes when implemented on a distributed system.