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Abstract: A class of pre-symmetric minimal residual method to solve large-scale system of linear algebraic equations with indefinite symmetrizable coefficient matrix is presented in this paper, briefly called as PSMINRES method. The PSMINRES method is established by first transforming the non-symmetric system of equations into symmetric system of equations by the pre-symmetric technique, and then utilizing the minimal residual (MINRES) method to solve the symmetric system of equations and getting a new approximation to the original system of linear equations. Theoretical analysis and numerical computations show that the pre-symmetric technique is feasible and behaviors of the PSMINRES are superior to some Krylov subspace methods, which are usual adopted for solving general non-symmetric linear systems, such as CGS, GMRES, etc. [Copyright &y& Elsevier]

Abstract: An improved regula falsi iterative formula for solving nonlinear equations is proposed in this paper. This method is effective and promising with its third-order convergence of both the sequences of diameters and iterative points sequence. [Copyright &y& Elsevier]

Abstract: In this paper, under the hypothesis that derivative satisfies some kinds of weak Lipschitz condition, the radius estimates of the convergence balls of secant type methods for operator equations are established in Banach space. Some applications and numerical experiments are also given. [Copyright &y& Elsevier]

Abstract: A class of regularized conjugate gradient methods is presented for solving large-scale sparse system of linear equations of which the coefficient matrix is an ill-conditioned skew-symmetric indefinite matrix. The convergence is proved and the possible choices of the parameters involved in the new methods are discussed in detail. Preliminary numerical computations show that the numerical behaviors of the new methods are superior to those of some standard Krylov subspace methods, such as CGNE, CGS, GMRES etc. [Copyright &y& Elsevier]

Abstract: In this study, a modification of the classical Secant method for solving nonlinear, univariate and unconstrained optimization problems based on the development of the cubic approximation is presented. The iteration formula including an approximation of the third derivative of f(x) by using the Taylor series expansion is derived. The performance of the new method is analyzed in terms of the number of iterations in comparison with the Secant methods using six test functions. [Copyright &y& Elsevier]

Abstract: This paper employs two new iterative methods accelerating convergence after using the classical regula falsi methods, such that both the sequence of diameters and the sequence of iteration produced by the new methods quadratically converge to zero. The numerical experiments show that new methods are effective and comparable to some well-known methods. [Copyright &y& Elsevier]

Abstract: Some new iterative formulae having three-order convergence are discussed in this paper. The theoretical analysis and numerical experiments show that new iterative formulae are effective and comparable to well-known method of Newton and Stefensen method. [Copyright &y& Elsevier]

Abstract: A class of exponential iterative formulae having quadratic convergence is discussed in this paper. The theoretical analysis and numerical experiments show that new exponential iterative formulae are effective and comparable to well-known method of Newton. [Copyright &y& Elsevier]

Abstract: In this paper, we study the convergence of Gauss–Newton’s method for nonlinear least squares problems. Under the hypothesis that derivative satisfies some kinds of weak Lipschitz condition, we obtain the exact estimates of the radii of convergence ball of Gauss–Newton’s method and the uniqueness ball of the solution. New results can be used to determinate approximation zero of Gauss–Newton’s method. [Copyright &y& Elsevier]