Application of Conjugate Gradient Method for the Solution of Large Matrix Problems

  • Tapan K. Sarkar
  • Saila Ponnapalli
  • Peter Petre


The conjugate gradient method (CGM) has found a wide variety of applications in electromagnetics and in signal processing. In addition, CGM when used in conjunction with FFT (CGFFT) is extremely efficient for solving Hankel and Toeplitz or block Toeplitz matrix systems which frequently arise in both electromagnetics and signal processing applications. The FFT may be utilized because of the convolutional nature of the matrix. CGM has also been used in adaptive spectral estimation. In this paper, a novel application of the conjugation gradient method in the determination of far-field antenna patterns via a near-field to far-field transformation will be discussed.


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  1. [1]
    T. K. Sarkar, K. R. Siarkiewicz, and R. F. Stratton, “Survey of numerical methods for solution of large systems of linear equations for electromagnetic field problems”, IEEE Trans on Antennas and Propagat., vol. AP-29, pp. 847–856, Nov. 1981.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    T. K. Sarkar, E. Arvas, and S. M. Rao, “Application of FFT and the conjugate gradient method for the solution of electromagetic radiation for electrically large and small conducting bodies”, IEEE Trans on Antennas and Propagat., vol. AP-34, pp. 635–640, May 1986.ADSCrossRefGoogle Scholar
  3. [3]
    C. C. Su, “Calculation of electromagnetic scattering from a dielectric cylinder using the Conjugate Gradient Method and FFT”, IEEE Trans. on Antennas and Propagat5., vol. AP-3, pp. 1418–1425, Dec. 1987.ADSGoogle Scholar
  4. [4]
    Su, C. C., “Electromagnetic scattering by a dielectric body with arbitrary inhomogeneity and anistropy”, IEEE Trans. on Antennas and Propagat., vol. AP-37, 384–389, Mar. 1989.ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    M. F. Catedra, E. Gago, and L. Nuno, “A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the Conjugate Gradient Method and the Fast Fourier Transform”, IEEE Trans on Antennas and Propagat., vol. AP-37, pp. 528–537, May, 1989.ADSCrossRefGoogle Scholar
  6. [6]
    T. K. Sarkar and X. Yang, “Efficient solution of Hankel systems utilizing FFTs and the Conjugate Gradient Method”, Proc. of International Conf. on Acoustics, Speech and Signal Processing (ICASSP 86), Dallas, TX, pp. 1835–1838, May 1987.Google Scholar
  7. [7]
    H. Chen, T. K. Sarkar, S. A. Dianat and J. D. Brule, “Adaptive spectral estimation by the Conjugate Gradient Method”, IEEE Trans. on ASSP, vol. ASSP-34, pp. 272–283, Apr. 1986.CrossRefGoogle Scholar
  8. [8]
    T. K. Sarkar, S. Ponnapalli and E. Arvas, “An accurate, efficient method of computing far-field antenna patterns from near-field measurements”, Proc. of International Conf. on Antennas and Propagation (AP-S 90), Dallas, TX, May 1990.Google Scholar
  9. [9]
    S. Ponnapalli, “The Computation of Far-field Antenna Patterns from Near-field Measurements Using an Equivalent Current Approach”, Ph.D. dissertation, Syracuse University, December 1990.Google Scholar
  10. [10]
    S. Ponnapalli, “Near-field to far-field transformation utilizing the conjugate gradient method”, in Application of Conjugate Gradient Method in Electromagnetics and Signal Processing, vol. 5 in PIER, T. K. Sarkar, ED. New York: VNU Science Press, Ch. 11, December 1990.Google Scholar
  11. [11]
    S. Ponnapalli and T. K. Sarkar, “Near-field to far-field transformation using an equivalent current approach”, submitted to IEEE Trans. on MTT, September 1990.Google Scholar
  12. [12]
    J. Brown and E. V. Jull, “The prediction of aerial radiation patterns from near-field measurements”, Proc. Inst. Elec. Eng., vol. 108B, pp. 635–644, Nov. 1961.Google Scholar
  13. [13]
    D. M. Kerns, “Plane-wave scattering-matrix theory of antennas and antennas-antenna interaction”, NBS Monograph 162, U.S. Govt. Printing Office, Washington, DC, June 1981.Google Scholar
  14. [14]
    F. Jensen, “Electromagnetic near-field far-field correlations”, Ph.D. dissertation, Techn. Univ. Denmark, July 1970.Google Scholar
  15. [15]
    P. F. Wacker, “Near-field antenna measurements using a spherical scan: efficient dat reduction with probe correction”, in Inst. Elec. Eng. Conf. Publi. 113, Conf. Precision Electromagn. Measurements, London, July 1974, pp. 286–288.Google Scholar
  16. [16]
    P. F. Wacker, “Non-planar near-field measurements: spherical scanning”, NBSIR 75–809, June 1975.Google Scholar
  17. [17]
    W. M. Leach and D. T. Paris, “Probe-compensated near-field measurements on a cylinder”, IEEE Trans. on Antennas and Propagat., vol. AP-21, pp. 435–445, July 1973.ADSCrossRefGoogle Scholar
  18. [18]
    R. F. Harrington, “Field Computation by Moment Methods”, Malabar: Robert E. Kreiger Publishing, 1968.Google Scholar
  19. [19]
    D. T. Paris, W. M. Leach, and E. B. Joy, “Basic theory of probe-compensated near-field measurements”, IEEE Trans. Antennas and Propagat., vol. Ap-26, pp. 373–379, May 1978.ADSCrossRefGoogle Scholar
  20. [20]
    R. E. Collin and F. J. Zucker, Antenna Theory, Part I., New York: McGraw-Hill, 4, 1969.Google Scholar
  21. [21]
    A. V. Oppenheim and R. W. Shafer, “Digital Signal Processing”, Englewood Cliffs, NJ: Prentice-Hall, 1975.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Tapan K. Sarkar
    • 1
  • Saila Ponnapalli
    • 1
  • Peter Petre
    • 1
  1. 1.Department of Electrical and Computer EngineeringSyracuse UniversitySyracuseUSA

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