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Speedup of tridiagonal system solvers. (English) Zbl 07241274
Summary: The paper proposes a new approach to the solution of standard and block tridiagonal systems that appear in various areas of technical, scientific and financial practice. Its goal is to elaborate an efficient two-phase tridiagonal solver, the particular case of which is the \(k\)-step cyclic reduction. The main idea of the proposed approach to designing a two-phase tridiagonal solver lies in using new model equations for dyadic system reduction. The resulting solver differs from the known two-phase partitioning ones also in the second phase, since it uses a series of simple explicit formulas for calculation of the remaining unknown values. Computational experiments on measuring speedup confirmed the efficiency of the proposed solver.
65 Numerical analysis
90 Operations research, mathematical programming
Full Text: DOI
[1] de Boor, C., Bicubic spline interpolation, J. Math. Phys., 41, 3, 212-218 (1962) · Zbl 0108.27103
[2] Hoffmann, W.; Sauer, T., A spline optimization problem from robotics, Rediconti Math., 26, 221-230 (2006) · Zbl 1120.41011
[3] Török, C.s., On reduction of equations’ number for cubic splines, Mat. Modelirovanie, 26, 11 (2014)
[4] Kačala, V.; Miňo, L.; Török, C.s., Speedup of uniform bicubic spline interpolation, (ITAT 2018: Information Technologies. ITAT 2018: Information Technologies, Applications and Theory (2018)), 3-9
[5] V. Kačala, C.s. Török, Speedup of bicubic spline interpolation, in: Computational Science - ICCS 2018 Part II, 2018, pp. 806-818.
[6] C.s. Török, Speedup of interpolating spline construction, in: Communication of the Joint Institute for Nuclear Research, Dubna, E11-2018-43, 2018.
[7] Buzbee, B. L.; Golub, G. H.; Nielson, C. W., On direct methods for solving Poisson’s equations, SIAM J. Numer. Anal., 7, 4, 627-656 (1970) · Zbl 0217.52902
[8] Bini, D.; Meini, B., The cyclic reduction algorithm, Numer. Algorithms, 51, 23-60 (2009) · Zbl 1170.65021
[9] Yalamov, P.; Pavlov, V., Stability of the block cyclic reduction, Linear Algebra Appl., 249, 341-358 (1996) · Zbl 0862.65016
[10] Intel Corporation, Intel® math kernel library documentation (2018)
[11] Fernando, K. V., Accurate BABE factorisation of tridiagonal matrices for eigenproblems (1995)
[12] Björck, A., Numerical Methods in Matrix Computations (2015), Springer · Zbl 1322.65047
[13] Buneman, O., A Compact Non-Iterative Poisson SolverTechnical Report SUIPR Rep. 294 (1969), Institue for Plasma Research, Stanford University: Institue for Plasma Research, Stanford University Paolo Alto, California
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