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Error analysis of the mdLVs algorithm for computing bidiagonal singular values. (English) Zbl 1259.65066
The authors analyze the perturbations on singular values and the forward errors of the modified discrete Lotka-Volterra (mdLV) variables, which occur in the mdLVs algorithm, through two kinds of error analysis in floating point arithmetic. They prove the forward stability of the mdLV algorithm in the sense of Bueno-Marcellan-Dopico.

65F20 Numerical solutions to overdetermined systems, pseudoinverses
Full Text: DOI
[1] Bueno, M.I., Marcellan, F.: Darboux transformation and perturbation of linear functionals. Linear Algebra Appl. 384, 215–242 (2004) · Zbl 1055.42016 · doi:10.1016/j.laa.2004.02.004
[2] Bueno, M.I., Dopico, F.M.: A more accurate algorithm for computing the Christoffel transformation. J. Comput. Appl. Math. 205, 567–582 (2007) · Zbl 1120.65050 · doi:10.1016/j.cam.2006.05.027
[3] Chaitin-Chatelin, F., Fraysse, V.: Lectures on Finite Precision Computations. SIAM, Philadelphia (1996) · Zbl 0846.65020
[4] Demmel, J., Kahan, W.: Accurate singular values of bidiagonal matrices. SIAM J. Sci. Statist. Comput. 11, 873–912 (1990) · Zbl 0705.65027 · doi:10.1137/0911052
[5] Fernando, K.V., Parlett, B.N.: Accurate singular values and differential qd algorithms. Numer. Math. 67, 191–229 (1994) · Zbl 0814.65036 · doi:10.1007/s002110050024
[6] Higham, N.J.: Accuracy and Stability of Numerical Algorithms, 2nd edn. SIAM, Philadelphia (2002) · Zbl 1011.65010
[7] Hirota, R.: Conserved quantities of a random-time Toda equation. J. Phys. Soc. Jpn. 66, 283–284 (1997) · Zbl 0942.82014 · doi:10.1143/JPSJ.66.283
[8] Iwasaki, M., Nakamura, Y.: On the convergence of a solution of the discrete Lotka–Volterra system. Inverse Probl. 18, 1569–1578 (2002) · Zbl 1021.35115 · doi:10.1088/0266-5611/18/6/309
[9] Iwasaki, M., Nakamura, Y.: An application of the discrete Lotka–Volterra system with variable step-size to singular value computation. Inverse Probl. 20, 553–563 (2004) · Zbl 1057.65018 · doi:10.1088/0266-5611/20/2/015
[10] Iwasaki, M., Nakamura, Y.: Accurate computation of singular values in terms of shifted integrable schemes. Jpn. J. Ind. Appl. Math. 23, 239–259 (2006) · Zbl 1117.65055 · doi:10.1007/BF03167593
[11] Iwasaki, M., Nakamura, Y.: Positivity of dLV and mdLVs algorithms for computing singular values. Elec. Trans. Numer. Anal. 38, 184–201 (2011) · Zbl 1287.65028
[12] Parlett, B.N.: The new qd algorithm. Acta Numer. 4, 459–491 (1995) · Zbl 0835.65059 · doi:10.1017/S0962492900002580
[13] Rutishauser, H.: Lectures on Numerical Mathematics. Brinkhäuser, Boston (1990)
[14] Spiridonov, V., Zhedanov, A.: Discrete-time Volterra chain and classical orthogonal polynomials. J. Phys. A.: Math. Gen. 30, 8727–37 (1997) · Zbl 0928.39007 · doi:10.1088/0305-4470/30/24/031
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