14 papers · ranked by Valyu relevance
J. L. Nazareth
A recalibration is proposed for "numerical analysis" as it arises specifically within the broader, embracing field of modern computer science (CS). This would facilitate research into theoretical and practicable models of real-number computation at the foundations of CS, and it would also advance the instructional…
Davoud Mirzaei
| 4 | 2 Davoud Mirzaei 0 2 Uppsala University c e D June 10, 2024 7 2 Contents O] H 1 What is scientific computing? 1 h. 1.1 Computational simulation 2 at m 2 Sources of approximation 4 [ 2.1 Absolute and relative errors 7 v1 8 3 Computer representation of numbers 7 5 9 3.1 Fixed-point representation of numbers 8 9 1…
Desmond J. Higham
I give a brief, non-technical, historical perspective on numerical analysis and optimization. I also touch on emerging trends and future challenges. This content is based on the short presentation that I made at the opening ceremony of The International Conference on Numerical Analysis and Optimization, which was held…
Ronald F. Boisvert, Michael J. Donahue, Daniel W. Lozier, Robert McMichael + 1 more
'Robert McMichael' 'Bert W. Rust'] In this paper we describe the role that mathematics plays in measurement science at NIST. We first survey the history behind NIST’s current work in this area, starting with the NBS Math Tables project of the 1930s. We then provide examples of more recent efforts in the application of…
Farah Benmouhoub, P. Garoche, Matthieu Martel
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of computation, used everywhere, is the sum of a sequence of numbers. This sum is…
Yong Li, Gonglin Yuan, Zengxin Wei, Zi-Ke Zhang
In this paper, a trust-region algorithm is proposed for large-scale nonlinear equations, where the limited-memory BFGS (L-M-BFGS) update matrix is used in the trust-region subproblem to improve the effectiveness of the algorithm for large-scale problems. The global convergence of the presented method is established…
Xiangrong Li, Xupei Zhao, Xiabin Duan, Xiaoliang Wang + 1 more
'Hans A Kestler'] It is generally acknowledged that the conjugate gradient (CG) method achieves global convergence-with at most a linear convergence rate-because CG formulas are generated by linear approximations of the objective functions. The quadratically convergent results are very limited. We introduce a new PRP…
Srinivasarao Thota, Vivek Kumar Srivastav
Objectives The present paper describes a new algorithm to find a root of non-linear transcendental equations. It is found that Regula-Falsi method always gives guaranteed result but slow convergence. However, Newton-Raphson method does not give guaranteed result but faster than Regula-Falsi method. Therefore, the…
Karine Chemla
Ancient sources attest to the introduction of two families of numeration systems using place-value notations. In such systems, the base and its powers are always represented using position. The existence of a base of this kind is reflected by the repetitive character of the algorithms drawing on the place-value…
Abinand Gopal, Vladimir Rokhlin
We introduce an efficient scheme for the construction of quadrature rules for bandlimited functions. While the scheme is predominantly based on well-known facts about prolate spheroidal wave functions of order zero, it has the asymptotic CPU time estimate O(n log n) to construct an n-point quadrature rule. Moreover…
Gonglin Yuan, Zhou Sheng, Wenjie Liu, Hans A Kestler
In this paper, the Hager and Zhang (HZ) conjugate gradient (CG) method and the modified HZ (MHZ) CG method are presented for large-scale nonsmooth convex minimization. Under some mild conditions, convergent results of the proposed methods are established. Numerical results show that the presented methods can be better…
Mariusz Pleszczyński, Robertas Damaševičius
Computer tomography has a wide field of applicability; however, most of its applications assume that the data, obtained from the scans of the examined object, satisfy the expectations regarding their amount and quality. Unfortunately, sometimes such expected data cannot be achieved. Then we deal with the incomplete set…
Salima Kouser, Shafiq Ur Rehman, Yasser Elmasry, Waqar Azeem Khan + 3 more
'Fayyaz Ahmad' 'Hamza Khan' 'B. Omkar Lakshmi Jagan'] The Newton method is a classical method for solving systems of nonlinear equations and offers quadratic convergence. The order of convergence of the Newton method is optimal as it requires one evaluation for the system of nonlinear equations and the second for the…
В. В. Аристов, А. В. Строганов
The well-known Turing machine is an example of a theoretical digital computer, and it was the logical basis of constructing real electronic computers. In the present paper we propose an alternative, namely, by formalising arithmetic operations in the ordinary computing device, we attempt to go to the analytical…