We analyze iterative processes of type xk+1 = xk - π(xk, Ek)F(xk) for solving F(x) = 0, F:Rn → Rm, m ≤ n. Parameters Ek are updated at each iteraction using least-change secant update procedures. We prove local, linear and superlinear convergence results. We introduce two new superlinearly convergent methods of this type, and one linearly convergent Quasi-Newton generalization of Cimmino's parallel algorithm for solving linear systems. Some numerical experiments are presented. © 1991.342171190Brent, Some Efficient Algorithms for Solving Systems of Nonlinear Equations (1973) SIAM Journal on Numerical Analysis, 10, pp. 327-344Brown, A Quadratically Convergent Newton-Like Method Based Upon Gaussian Elimination (1969) SIAM Journal on Numerical Analysis, 6, pp. 560-569Broyden, A class of methods for solving nonlinear simultaneous equations (1965) Mathematics of Computation, 19, pp. 577-593Broyden, The convergence of an algorithm for solving sparse nonlinear systems (1971) Mathematics of Computation, 25, pp. 285-294Broyden, Dennis, Jr, Moré, On the local and superlinear convergence of quasi-Newton methods (1973) J. Inst. Math. Appl., 12, pp. 223-245Cimmino, Calcolo approssimato per le soluzioni dei sistemi di equazioni lineari (1938) Ricerca Sci. Ser II, 4 (1), pp. 326-333Dennis, Jr, Moré, A characterization of superlinear convergence and its application to quasi-Newton methods (1974) Mathematics of Computation, 28, pp. 549-560Dennis, Jr, Moré, Quasi-Newton Methods, Motivation and Theory (1977) SIAM Review, 19, pp. 46-89Dennis, Jr, Schnabel, Least Change Secant Updates for Quasi-Newton Methods (1979) SIAM Review, 21, pp. 443-459Dennis, Jr, Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983) Prentice-Hall Ser. Comput. Math., , Prentice-Hall, Englewood Cliffs,NJDennis, Jr, Walker, Convergence Theorems for Least-Change Secant Update Methods (1981) SIAM Journal on Numerical Analysis, 18, pp. 949-987Gay, Brown's method and some generalizations with applications to minimization problems (1975) TR75-225, Dept. Comput. Sci.,, , Cornell Univ, Ithaca, NYGolub, Van Loan, (1983) Matrix Computations, , Johns Hopkins Univ. Press, Baltimore, MDGreenstadt, Variations on variable-metric methods (1970) Math. Comp., 24, pp. 1-22Griewank, Toint, On the unconstrained optimization of partially separable functions (1981) Nonlinear Optimization, , M.J.D. Powell, Academic Press, New YorkGriewank, Toint, Partitioned variable metric for large structured optimization problems (1982) Numer. Math., 39, pp. 119-137Griewank, Toint, Local convergence analysis for partitioned quasi-Newton updates (1982) Numer. Math., 39, pp. 429-448Griewank, Toint, Numerical experiments with partially separable optimization problems (1984) Numerical Analysis, Proceedings Dundee 1983, 1066, pp. 203-220. , D.F. Griffiths, Springer, Berlin, Lecture Notes in MathKarmarkar, A new polynomial-time algorithm for linear programming (1984) Combinatorica, 4, pp. 373-395Martínez, Generalization of the Methods of Brent and Brown for Solving Nonlinear Simultaneous Equations (1979) SIAM Journal on Numerical Analysis, 16, pp. 434-448Martínez, Solving nonlinear simultaneous equations with a generalization of Brent's method (1980) BIT, 20, pp. 501-510Martínez, Solution of nonlinear systems of equations by an optimal projection method (1986) Computing, 37, pp. 59-70Martínez, Sampaio, Parallel and sequential Kaczmarz methods for solving underdetermined nonlinear equations (1986) J. Comput. Appl. Math., 15 (3), pp. 311-321Marwil, Exploiting sparsity in Newton-type methods (1978) Ph.D. Thesis, , Cornell Univ, Ithaca, NYMarwil, Convergence Results for Schubert’s Method for Solving Sparse Nonlinear Equations (1979) SIAM Journal on Numerical Analysis, 16, pp. 588-604Meyn, Solution of underdetermined nonlinear equations by stationary methods (1983) Numer. Math., 42, pp. 161-172Ortega, Rheinboldt, (1970) Iterative Solution of Nonlinear Equations in Several Variables, , Academic Press, New YorkPowell, A new algorithm for unconstrained optimization (1970) Nonlinear Programming, , J.B. Rosen, O.L. Mangasarian, K. Ritter, Academic Press, New YorkSchubert, Modification of a quasi-Newton method for nonlinear equations with a sparse Jacobian (1970) Mathematics of Computation, 24, pp. 27-30Schwetlick, (1978) Numerische Lösung nichtlinearer Gleichungen, , Deutscher Verlag der Wissenschaften, BerlinToint, On sparse and symmetric matrix updating subject to a linear equation (1977) Mathematics of Computation, 31, pp. 954-961Toint, Numerical solution of large sets of algebraic nonlinear equations (1986) Mathematics of Computation, 46, pp. 175-189Walker, Watson, Least change secant update methods for underdetermined systems (1989) Research Report, , Dept. Math., Utah State Univ, UT