An efficient algorithm for multivariate Maclaurin-Newton transformation
نویسنده
چکیده
This paper presents explicit formulae for multivariate Maclaurin-Lagrange M : Kn1×n2×...×nd → Kn1×n2×...×nd and Maclaurin-Newton P : Kn1×n2×...×nd → Kn1×n2×...×nd transformations with respect to points whose coordinates form geometric sequences. Moreover, efficient algorithms for these transformations are given. Both of them perform computations with a running time of O (∏d j=1 nj · log ∏d j=1 nj ) +O ( d ∏d j=1 nj ) .
منابع مشابه
SIZING OPTIMIZATION OF TRUSS STRUCTURES WITH NEWTON META-HEURISTIC ALGORITHM
This study is devoted to discrete sizing optimization of truss structures employing an efficient discrete evolutionary meta-heuristic algorithm which uses the Newton gradient-based method as its updating scheme and it is named here as Newton Meta-heuristic Algorithm (NMA). In order to enable the NMA population-based meta-heuristic to effectively explore the discrete design space, a term contain...
متن کاملA Trust Region Algorithm for Solving Nonlinear Equations (RESEARCH NOTE)
This paper presents a practical and efficient method to solve large-scale nonlinear equations. The global convergence of this new trust region algorithm is verified. The algorithm is then used to solve the nonlinear equations arising in an Expanded Lagrangian Function (ELF). Numerical results for the implementation of some large-scale problems indicate that the algorithm is efficient for these ...
متن کاملConvexity results and sharp error estimates in approximate multivariate integration
An interesting property of the midpoint rule and trapezoidal rule, which is expressed by the so-called Hermite–Hadamard inequalities, is that they provide one-sided approximations to the integral of a convex function. We establish multivariate analogues of the Hermite–Hadamard inequalities and obtain access to multivariate integration formulae via convexity, in analogy to the univariate case. I...
متن کاملDirections for computing truncated multivariate Taylor series
Efficient recurrence relations for computing arbitrary-order Taylor coefficients for any univariate function can be directly applied to a function of n variables by fixing a direction in Rn. After a sequence of directions, the multivariate Taylor coefficients or partial derivatives can be reconstructed or “interpolated”. The sequence of univariate calculations is more efficient than multivariat...
متن کاملAn efficient improvement of the Newton method for solving nonconvex optimization problems
Newton method is one of the most famous numerical methods among the line search methods to minimize functions. It is well known that the search direction and step length play important roles in this class of methods to solve optimization problems. In this investigation, a new modification of the Newton method to solve unconstrained optimization problems is presented. The significant ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Annales UMCS, Informatica
دوره 8 شماره
صفحات -
تاریخ انتشار 2008