Sparsity in large-scale network computation

Control and Dynamic Systems

Volumn 41, Issue P1, 1991, Pages 207-272

  Alvarado, Fernando L ^a   Tinney, William F ^b   Enns, Mark K ^c  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b Head and Neck Institute   (United States)

^c Electrocon International Inc   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 68349148413     PISSN: 00905267     EISSN: None     Source Type: Book Series    
DOI: 10.1016/B978-0-12-012741-2.50009-9     Document Type: Chapter

References (53)

1. Alvarado, F.L., “Computational complexity in power systems,”. IEEE Transactions on Power Apparatus and Systems PAS-95:no. 3 (May/June 1976), 1080–1090.
2. Sato, N., Tinney, W., “Techniques for exploiting the sparsity of the network admittance matrix,”. IEEE Transactions on Power Apparatus and Systems 82 (December 1963), 944–950.
3. W. Tinney and J. Walker, “Direct solutions of sparse network equations by optimally ordered triangular factorization,” Proceedings of the IEEE, vol. 55, no. 11, pp. 1801–1809, November 1967.
4. IBM Corporation, Symposium on Sparse Matrices and their Applications, Yorktown Heights, New York, September 1968.
5. K. Takahashi, J. Fagan, and M.-S. Chen, “Formation of a sparse bus impedance matrix and its application to short circuit study,” in Power Industry Computer Applications Conference, pp. 63–69, May 1973.
6. George, A., Liu, J.W.H., “The evolution of the minimum degree ordering algorithm,”. SIAM Review 31 (March 1989), 1–19.
7. Bunch, J., Parlett, B., “Direct methods for solving symmetric indefinite systems of linear equations,”. SIAM Journal of Numerical Analysis 8 (1971), 639–655.
8. Duff, I.S., Reid, J.K., Munksgaard, N., Nielsen, H.B., “Direct solution of sets of linear equations whose matrix is sparse, symmetric and indefinite,”. Journal of the Institute of Mathematics and its Applications 23 (1979), 235–250.
9. G. Hachtel, Sparse Matrix Computations, chapter The Sparse Tableau Approach to Finite Element Assembly, pp. 349–363, SIAM Journal of Numerical Analysis, 1976.
10. Alvarado, F.L., Reitan, D.K., Bahari-Kashani, M., “Sparsity in diakoptic algorithms,”. IEEE Transactions on Power Apparatus and Systems PAS–96:no. 5 (September/October 1977), 1450–1459.
11. F. F. Wu, “Diakoptic network analysis,” in Power Industry Computer Applications Conference, pp. 364–371, June 1975.
12. Alsaç, O., Stott, B., Tinney, W., “Sparsity-oriented compensation methods for modified network solutions,”. IEEE Transactions on Power Apparatus and Systems PAS-102:no. 5 (May 1983), 1050–1060.
13. Chan, S.M., Brandwajn, V., “Partial matrix refactorization,”. IEEE Transactions on Power Systems PWRS-1:no. 1 (February 1986), 193–200.
14. Tinney, W., Brandwajn, V., Chan, S., “Sparse vector methods,”. IEEE Transactions on Power Apparatus and Systems PAS-104:no. 2 (February 1985), 295–301.
15. Alvarado, F.L., Mong, S.K., Enns, M.K., “A fault program with macros, monitors, and direct compensation in mutual groups,”. IEEE Transactions on Power Apparatus and Systems PAS-104:no. 5 (May 1985), 1109–1120.
16. Betancourt, R., “An efficient heuristic ordering algorithm for partial matrix refactorization,”. IEEE Transactions on Power Systems 3:no. 3 (August 1988), 1181–1187.
17. Gomez, A., Franquelo, L., “Node ordering algorithms for sparse vector method improvement,”. IEEE Transactions on Power Systems 3:no. 1 (February 1988), 73–79.
18. van Amerongen, R.A., “A rank-oriented setup for the compensation algorithm,”. IEEE Transactions on Power Systems 5:no. 1 (February 1990), 283–288.
19. Enns, M.K., Tinney, W.F., Alvarado, F.L., “Sparse matrix inverse factors,”. IEEE Transactions on Power Systems 5:no. 2 (May 1990), 466–473.
20. Alvarado, F.L., Yu, D.C., Betancourt, R., “Partitioned sparse A−1 methods,”. IEEE Transactions on Power Systems 5:no. 2 (May 1990), 452–459.
21. F. L. Alvarado and M. K. Enns, “Blocked sparse matrices in electric power systems,” Paper A 76–362, IEEE PES Summer Meeting, Portland, Oregon, July 18–23, 1976.
22. Alvarado, F.L., Tinney, W.F., “State estimation using augmented blocked matrices,”. IEEE Transactions on Power Systems 5:no. 3 (August 1990), 911–921.
23. R. R. Nucera and M. L. Gilles, “A blocked sparse matrix formulation for the solution of equality-constrained state estimation,” IEEE Transactions on Power Systems, 1990. Presented at the IEEE Power Engineering Society 1990 Winter Meeting.
24. Bacher, R., Tinney, W., “Faster local power flow solutions: the zero mismatch approach,”. IEEE Transactions on Power Systems 4:no. 4 (November 1989), 1345–1354.
25. Alvarado, F.L., “Symmetric matrix primitization,”, November 1989, The University of Wisconsin–Madison Technical Report ECE-89–19.
26. Grcar, J.F., “Matrix stretching for linear equations,”, November 1990, Sandia National Laboratories Technical Report SAND90–8723.
27. Tylavsky, D.J., Bose, A., Alvarado, F.L., Betancourt, R., Clemens, K., Heydt, G., Huang, G., Ilic, M., LaScala, M., Pai, M., Pottle, C., Talukdar, S., VanNess, J., Wu, F., “Parallel processing in power system computation,”. IEEE Transactions on Power Systems, 1991 In preparation.
28. A. Sherman, On the Efficient solution of Sparse Linear and Nonlinear Equations, PhD thesis, Yale University, Department of Computer Science, 1975. Report 46.
29. Pissanetsky, S., Sparse matrix technology, 1984, Academic Press.
30. F. L. Alvarado, “A note on sorting sparse matrices,” Proceedings of the IEEE, vol. 67, no. 9, pp. 1362–1363, September 1979.
31. Speelpenning, B., “The generalized element method,”, 1978, University of Illinois at Urbana-Champaign Technical Report UIUCDCS-R-78–946.
32. George, J.A., McIntyre, D.R., “On the application of the minimum degree algorithm to finite element systems,”. SIAM Journal of Numerical Analysis 15 (1978), 90–111.
33. Liu, J.W.H., “Modification of the minimum degree algorithm by multiple elimination,”. ACM Transactions on Mathematical Software 11 (1985), 141–153.
34. Betancourt, R., Alvarado, F.L., “Parallel inversion of sparse matrices,”. IEEE Transactions on Power Systems PWRS-1:no. 1 (February 1986), 74–81.
35. Alvarado, F.L., “Formation of y-node using the primitive y-node concept,”. IEEE Transactions on Power Apparatus and Systems PAS-101:no. 12 (December 1982), 4563–4571.
36. W. Tinney, W. Powell, and N. Peterson, “Sparsity-oriented network reduction,” in Power Industry Computer Applications Conference, pp. 384–390, May 1973.
37. Tinney, W.F., Bright, J.M., “Adaptive reductions for power flow equivalents,”. IEEE Transactions on Power Systems PWRS-2:no. 2 (May 1987), 351–360.
38. M. K. Enns and J. J. Quada, “Sparsity-enhanced network reduction for fault studies,” IEEE Transactions on Power Systems, July 1990. Presented at the IEEE Power Engineering Society 1990 Summer Meeting, Minneapolis, Minnesota.
39. R. Bacher, G. C. Ejebe, and W. F. Tinney, “Approximate sparse vector techniques for power network solution,” in Power Industry Computer Applications Conference, pp. 2–8, May 1989. Seattle, Washington.
40. Sage, A.P., Melsa, J.L., Estimation Theory with Applications to Communications and control, 1971, McGraw-Hill.
41. Householder, A.S., The theory of matrices in numerical analysis, 1964, Blaisdell.
42. Liu, J.W., “Reordering sparse matrices for parallel elimination,”, 1987, Department of Computer Science, York University, Downsview, Ontario, Canada Technical Report CS-87–01.
43. Lewis, J.G., Peyton, B.W., Pothen, A., “A fast algorithm for reordering sparse matrices for parallel factorization,”. SIAM Journal on Scientific and Statistical Computing 10:no. 6 (November 1989), 1146–1173.
44. F. L. Alvarado and R. Schreiber, “Optimal parallel solution of sparse triangular systems,” SIAM Journal of Numerical Analysis, 1990. Submitted for publication.
45. Brandwajn, V., Tinney, W., “Generalized method of fault analysis,”. IEEE Transactions on Power Apparatus and Systems PAS-104:no. 6 (June 1985), 1301–1306.
46. Tinney, W., Hart, C., “Power flow solution by Newton's method,”. IEEE Transactions on Power Apparatus and Systems PAS-86:no. 11 (November 1967), 1449–1460.
47. Stott, B., Alsaç, O., “Fast decoupled load flow,”. IEEE Transactions on Power Apparatus and Systems PAS-93:no. 3 (May/June 1974), 859–869.
48. George, A., Liu, J.W., Computer Solution of Large Sparse Positive Definite Systems, 1981, Prentice-Hall.
49. Duff, I., Erisman, A., Reid, J., Direct Methods for Sparse Matrices, 1986, Clarendon Press.
50. Taylor, C.W., Farmer, R.J., “Eigenanalysis and frequency domain methods for system dynamic performance,”, 1990, IEEE Technical Report 90TH0292–3-PWR, Edited report.
51. I. S. Duff, “A survey of sparse matrix research,” Proceedings of the IEEE, vol. 65, pp. 500–535, April 1977.
52. July 1990. Special issue on Sparse Matrices.
53. Alvarado, F.L., “Manipulation and visualization of sparse matrices,”. ORSA Journal on Computing 2:no. 2 (spring 1990), 186–207.