Njia ya Conjugate Gradient
Njia ya Conjugate Gradient (CG) ni algorithmu ya marudio kwa ajili ya kutatua mifumo mikubwa ya mstari yenye uwazi na yenye uhakika chanya (symmetric positive-definite) ya Ax = b, iliyoandaliwa na Hestenes na Stiefel mwaka 1952. Ni mojawapo ya visuluhishi vya marudio vinavyotumiwa sana katika sayansi ya kompyuta kwa sababu inakamilika kwa zaidi ya iterashini n kwa matriksi ya n × n na kwa kawaida huhitaji kidogo zaidi.
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Vyanzo
- Hestenes, M. R., & Stiefel, E. (1952). Methods of conjugate gradients for solving linear systems. Journal of Research of the National Bureau of Standards, 49(6), 409–436. DOI: 10.6028/jres.049.044 ↗
- Saad, Y. (2003). Iterative Methods for Sparse Linear Systems (2nd ed.). SIAM. DOI: 10.1137/1.9780898718003 ↗
- Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer. DOI: 10.1007/978-0-387-40065-5 ↗
Jinsi ya kunukuu ukurasa huu
ScholarGate. (2026, June 3). Conjugate Gradient Method for Linear Systems. ScholarGate. https://scholargate.app/sw/numerical-methods/conjugate-gradient-method
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