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Methods for the solution of AXD-BXC=E and its application in the numerical solution of implicit ordinary differential equations. (English) Zbl 0452.65015


MSC:

65F05 Direct numerical methods for linear systems and matrix inversion
15A24 Matrix equations and identities
15A18 Eigenvalues, singular values, and eigenvectors
65L05 Numerical methods for initial value problems involving ordinary differential equations

Software:

Algorithm 432
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Full Text: DOI

References:

[1] F. R. Gantmacher,Theory of Matrices, Chelsea Publishing Co., New York, N.Y. (1977). · Zbl 0085.01001
[2] R. H. Bartels and G. W. Stewart, Algorithm 432,Solution of the matrix equation AX+XB=C, ACM, 15 (1972), 214–235. · Zbl 1372.65121 · doi:10.1145/361573.361582
[3] W. H. Enright,Improving the efficiency of matrix operations in the numerical solution of stiff ordinary differential equations. ACM Trans. Math. Software, 4, No. 2 (1978), 127–136. · Zbl 0382.65029 · doi:10.1145/355780.355784
[4] C. B. Moler and G. W. Stewart,An algorithm for generalized matrix eigenvalue problems, SIAM J. Num. Anal., 10, No. 2 (1973), 241–256. · Zbl 0253.65019 · doi:10.1137/0710024
[5] R. C. Ward,The combination shift QZ algorithm, SIAM J. Num. Anal., 12, No. 6 (1975), 835–853. · Zbl 0342.65022 · doi:10.1137/0712062
[6] L. Kaufmann,The LZ algorithm to solve the generalized eigenvalue problem, 11, No. 5 (1974), 997–1024. · Zbl 0294.65025
[7] J. C. Butcher,Implicit Runge-Kutta processes, Math. Comp., 18, (1964), 50–64. · Zbl 0123.11701 · doi:10.1090/S0025-5718-1964-0159424-9
[8] C. W. Gear,Simultaneous numerical solutions of differential-algebraic equations, IEEE Trans. Circuit Theory, CT-18, No. 1 (1971), 89–95. · doi:10.1109/TCT.1971.1083221
[9] T. A. Bickart and Z. Picel,High order stiffly stable composite multistep methods for numerical integration of stiff differential equations, BIT 13, (1973), 272–286. · Zbl 0265.65040 · doi:10.1007/BF01951938
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