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Nonlinear iterative methods and parallel computation. (English) Zbl 0356.65057


MSC:

65K05 Numerical mathematical programming methods
65H10 Numerical computation of solutions to systems of equations
90C30 Nonlinear programming

Software:

BRENT
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Full Text: EuDML

References:

[1] J. M. Ortega W. C. Rheinboldt: Iterative solution of nonlinear equations in several variables. AP, New York, 1970. · Zbl 0241.65046
[2] M. J. D. Powell: A survey of numerical methods for unconstrained optimization. SIAM Review, 1 (1970), 79-97. · Zbl 0218.90059
[3] D. Chazan W. Miranker: A nongradient and parallel algorithm for unconstrained minimization. SIAM J. Control, 2 (1970), 207-217. · Zbl 0223.65022
[4] D. M. Himmelblau: Decomposition of large-scale problems. North-Holl. publ. comp., New York, 1973. · Zbl 0254.90002
[5] R. M. Karp W. L. Miranker: Parallel minimax search for a maximum. J. of Combinatioral Theory, 1 (1968), 19-35. · Zbl 0153.47703
[6] R. P. Brent: Algorithms for minimization without derivatives. Prentice-Hall, Englewood Cliffs, New Jersey, 1973. · Zbl 0245.65032
[7] W. I. Zangwill: Minimizing a function without calculating derivatives. Comp. J., 7 (1967), 293-296. · Zbl 0189.48004
[8] M. J. D. Powell: An efficient method for finding minimum of a function of several variables without calculating derivatives. Compt. J., 7 (1964), 155- 162. · Zbl 0132.11702
[9] H. T. Kung J. F. Traub: On the efficiency of parallel iterative algorithms for non-linear equations. Symposium on complexity of sequential and parallel numerical algorithms, Cornegie-Mellon University, 1973.
[10] W. Miranker: Parallel methods for approximating the root of a function. IBM J. of Research and Development, vol. 13, 1967, 297-301. · Zbl 0177.20204
[11] S. Winograd: Parallel iteration methods, Complexity of computer computations. R. E. Miller and J. W. Thatcher, Plenum Press, New York, 1972, 53 - 60.
[12] N. Anderson A. Brörck: A new high order method of regula falsi type for computing a root of an equation. BIT, 13 (1973), 253-264. · Zbl 0263.65054
[13] F. Sloboda: A parallel projection method for linear algebraic systems. to appear. · Zbl 0398.65013
[14] F. Sloboda: Parallel method of conjugate directions for minimization. Apl. mat. 6 (1975), 436-446. · Zbl 0326.90050
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