Presenting the Lazy Evaluation of Functions

Thesis submitted for the degree of Doctor of philosoph

Evaluation of functions on microcomputers: rational approximation of kth roots

AbstractThis paper describes the implementation of rational approximation algorithms for evaluation of kth roots in short wordlength machines. The emphasis is on maintaining full machine precision in computers that use fixed point, truncated binary arithmetic with at most 16 bits of wordlength. Included is a table of coefficients for evaluation of kth roots on a 16 bit machine with 3 ≤ k ≤ 11

Efficient approximation of functions of some large matrices by partial fraction expansions

Some important applicative problems require the evaluation of functions $\Psi$ of large and sparse and/or \emph{localized} matrices $A$. Popular and interesting techniques for computing $\Psi(A)$ and $\Psi(A)\mathbf{v}$, where $\mathbf{v}$ is a vector, are based on partial fraction expansions. However, some of these techniques require solving several linear systems whose matrices differ from $A$ by a complex multiple of the identity matrix $I$ for computing $\Psi(A)\mathbf{v}$ or require inverting sequences of matrices with the same characteristics for computing $\Psi(A)$. Here we study the use and the convergence of a recent technique for generating sequences of incomplete factorizations of matrices in order to face with both these issues. The solution of the sequences of linear systems and approximate matrix inversions above can be computed efficiently provided that $A^{-1}$ shows certain decay properties. These strategies have good parallel potentialities. Our claims are confirmed by numerical tests

Evaluation of functions and values of Attica wetlands in Greece

The document is a synopsis of the Greek version and comprises the following chapters: Study areas: Brief description of the study areas: 1) Asopos estuary and Oropos lagoons, 2) Marathonas reservoir, 3) Sxinias national park, 4) Loutsa wetland, 5) Vravrona wetland, 6) Lake Vouliagmeni, 7) Lake Koumoundourou, 8) Vourkari wetland, and 9) Psatha wetland. Functional evaluation methodological approach: The WET method for the assessment of wetland functions and values and the HydroGeoMorphological approach (HGM) applied in two wetland sites, are presented. Assessment of wetland functions and values: The results of the functional assessment of Attiki’s wetlands are summarized in tables

Multi-party Function Evaluation with Perfectly Private Audit Trail

We propose an efficient and simple protocol for the evaluation of functions getting their inputs from multiple parties in a way that guarantees the correctness of the computation to everyone and the perfect privacy of the inputs as long as the worker is honest

MODIFIKASI METODE HANSEN-PATRICK DENGAN ORDE KONVERGENSI OPTIMAL UNTUK MENYELESAIKAN PERSAMAAN NONLINIER

The Hansen-Patrick method is a third-order  iterative  method used to solve nonlinear equation. The method requires three evaluation of functions and has an efficiency index 31/3 » 1,4224. This study discusses a modification of the Hansen-Patrick method using the second order Taylor series. The second derivative is reduced using hyperbolic function with one parameter h. The aim of modification is to improve the convergence order of the Hansen-Patrick’s method. Based on the convergence analysis, the method has a fourth-order of convergence and envolve three evaluation of functions. So, its efficiency index is 41/3 » 1,5874. Numerical simulation is given to illustrate performance  of the iterative method using six real functions. The performance of the iterative method include : a computational order of convergence, the number of iteration, evaluation of function, absolute error, and value of function, will be compared with Newton’s method, Halley’s method, Newton-Steffensen’s method, and Hansen-Patrick method. The numerical simulation shows that the performance of the method better than other

On range evaluation of functions applying interval analysis

制度:新 ; 文部省報告番号:甲2060号 ; 学位の種類:博士(情報科学) ; 授与年月日:2005/3/15 ; 早大学位記番号:新401

A Mathematical Basis for an Interval Arithmetic Standard

Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8