scholarly journals Continuity as a computational effect

2016 ◽  
Vol 85 (5) ◽  
pp. 1057-1085 ◽  
Author(s):  
Renato Neves ◽  
Luis S. Barbosa ◽  
Dirk Hofmann ◽  
Manuel A. Martins
Keyword(s):  
Computational Effect

scholarly journals Semidiscrete central difference method in time for determining surface temperatures

2005 ◽  
Vol 2005 (3) ◽  
pp. 393-400 ◽  
Author(s):  
Zhi Qian ◽  
Chu-Li Fu ◽  
Xiang-Tuan Xiong
Keyword(s):  
Difference Method ◽  
Heat Conduction Problem ◽  
A Priori ◽  
Inverse Heat Conduction Problem ◽  
The Body ◽  
Temperature History ◽  
Measured Temperature ◽  
Central Difference ◽  
Approximation Solution ◽  
Computational Effect

We consider an inverse heat conduction problem (IHCP) in a quarter plane. We want to know the distribution of surface temperature in a body from a measured temperature history at a fixed location inside the body. This is a severely ill-posed problem in the sense that the solution (if exists) does not depend continuously on the data. Eldén (1995) has used a difference method for solving this problem, but he did not obtain the convergence atx=0. In this paper, we gave a logarithmic stability of the approximation solution atx=0under a stronger a priori assumption‖u(0,t)‖p≤Ewithp>1/2. A numerical example shows that the computational effect of this method is satisfactory.

AN INFEASIBLE SSLE FILTER ALGORITHM FOR GENERAL CONSTRAINED OPTIMIZATION WITHOUT STRICT COMPLEMENTARITY

2011 ◽  
Vol 28 (03) ◽  
pp. 361-399 ◽  
Author(s):  
CHUNGEN SHEN ◽  
WENJUAN XUE ◽  
DINGGUO PU
Keyword(s):  
Linear Independence ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Active Set ◽  
Strict Complementarity ◽  
Complementarity Condition ◽  
Sequential Systems ◽  
Computational Effect ◽  
Systems Of Linear Equations ◽  
One Step

In this paper, we propose a new sequential systems of linear equations (SSLE) filter algorithm, which is an infeasible QP-free method. The new algorithm needs to solve a few reduced systems of linear equations with the same nonsingular coefficient matrix, and after finitely many iterations, only two linear systems need to be solved. Furthermore, the nearly active set technique is used to improve the computational effect. Under the linear independence condition, the global convergence is proved. In particular, the rate of convergence is proved to be one-step superlinear without assuming the strict complementarity condition. Numerical results and comparison with other algorithms indicate that the new algorithm is promising.

scholarly journals Online Type-Directed Partial Evaluation

1997 ◽  
Vol 4 (53) ◽  
Author(s):  
Olivier Danvy
Keyword(s):  
Pattern Matching ◽  
Experimental Work ◽  
Partial Evaluation ◽  
Meta Level ◽  
Computational Effect ◽  
Symbolic Evaluation ◽  
Compiled Code

In this experimental work, we extend type-directed partial evaluation (a.k.a. "reduction-free normalization" and "normalization by evaluation") to make it online, by enriching it with primitive operations (delta-rules). Each call to a primitive operator is either unfolded or residualized, depending on the operands and either with a default policy or with a user-supplied filter. The user can also specify how to residualize an operation, by pattern-matching over the operands. Operators may be pure or have a computational effect. <br />We report a complete implementation of online type-directed partial evaluation in Scheme, extending our earlier offline implementation.<br />Our partial evaluator is native in that it runs compiled code instead of using the usual meta-level technique of symbolic evaluation.

scholarly journals On stabilization of the node-based smoothed finite element method for free vibration problems

2010 ◽  
Vol 32 (3) ◽  
pp. 167-181
Author(s):  
Bui Xuan Thang ◽  
Nguyen Xuan Hung ◽  
Ngo Thanh Phong
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Vibration ◽  
Solid Mechanics ◽  
High Reliability ◽  
Free Vibration Analysis ◽  
Zero Energy ◽  
Computational Effect ◽  
Smoothed Finite Element Method ◽  
Element Method

The node-based smoothed finite element method (NS-FEM) has been recently proposed by Liu et al to enhance the computational effect for solid mechanics problems. However, it is evident that the NS-FEM behaves "overly-soft" and so it may lead to instability for dynamic problems. The instability can be clearly shown as spurious non-zero energy modes in free vibration analysis. In this paper, we present a stabilization of the node-based smoothed finite element method (SN-FEM) that is stable (no spurious non-zero energy modes) and more effective than the standard finite element method (FEM). Three numerical illustrations are given to evince the high reliability of the proposed formulation.

scholarly journals Algebras for weighted search

2021 ◽  
Vol 5 (ICFP) ◽  
pp. 1-30
Author(s):  
Donnacha Oisín Kidney ◽  
Nicolas Wu
Keyword(s):  
Dijkstra’S Algorithm ◽  
Breadth First Search ◽  
Essential Component ◽  
Probabilistic Sampling ◽  
Dijkstra's Algorithm ◽  
Wide Range ◽  
Computational Effect

Weighted search is an essential component of many fundamental and useful algorithms. Despite this, it is relatively under explored as a computational effect, receiving not nearly as much attention as either depth- or breadth-first search. This paper explores the algebraic underpinning of weighted search, and demonstrates how to implement it as a monad transformer. The development first explores breadth-first search, which can be expressed as a polynomial over semirings. These polynomials are generalised to the free semimodule monad to capture a wide range of applications, including probability monads, polynomial monads, and monads for weighted search. Finally, a monad transformer based on the free semimodule monad is introduced. Applying optimisations to this type yields an implementation of pairing heaps, which is then used to implement Dijkstra's algorithm and efficient probabilistic sampling. The construction is formalised in Cubical Agda and implemented in Haskell.

scholarly journals A Fuzzy Set Based Approach for Rating Bias

2019 ◽  
Vol 33 ◽  
pp. 9969-9970
Author(s):  
Mingming Li ◽  
Jiao Dai ◽  
Fuqing Zhu ◽  
Liangjun Zang ◽  
Songlin Hu ◽  
...  
Keyword(s):  
Fuzzy Set ◽  
Real World ◽  
Matrix Factorization ◽  
Sparse Matrix ◽  
Side Information ◽  
Initial Attempt ◽  
The Matrix ◽  
Computational Effect ◽  
Real World Datasets ◽  
The Membership Function

In recommender systems, the user uncertain preference results in unexpected ratings. This paper makes an initial attempt in integrating the influence of user uncertain degree into the matrix factorization framework. Specifically, a fuzzy set of like for each user is defined, and the membership function is utilized to measure the degree of an item belonging to the fuzzy set. Furthermore, to enhance the computational effect on sparse matrix, the uncertain preference is formulated as a side-information for fusion. Experimental results on three real-world datasets show that the proposed approach produces stable improvements compared with others.

scholarly journals A Functional Correspondence between Monadic Evaluators and Abstract Machines for Languages with Computational Effects

2004 ◽  
Vol 11 (28) ◽  
Author(s):  
Mads Sig Ager ◽  
Olivier Danvy ◽  
Jan Midtgaard
Keyword(s):  
Lambda Calculus ◽  
Abstract Machine ◽  
Error Handling ◽  
Abstract Machines ◽  
Computational Effect

We extend our correspondence between evaluators and abstract machines from the pure setting of the lambda-calculus to the impure setting of the computational lambda-calculus. We show how to derive new abstract machines from monadic evaluators for the computational lambda-calculus. Starting from (1) a generic evaluator parameterized by a monad and (2) a monad specifying a computational effect, we inline the components of the monad in the generic evaluator to obtain an evaluator written in a style that is specific to this computational effect. We then derive the corresponding abstract machine by closure-converting, CPS-transforming, and defunctionalizing this specific evaluator. We illustrate the construction first with the identity monad, obtaining the CEK machine, and then with a lifting monad, a state monad, and with a lifted state monad, obtaining variants of the CEK machine with error handling, state and a combination of error handling and state. <br /> <br />In addition, we characterize the tail-recursive stack inspection presented by Clements and Felleisen as a lifted state monad. This enables us to combine this stack-inspection monad with other monads and to construct abstract machines for languages with properly tail-recursive stack inspection and other computational effects. The construction scales to other monads--including one more properly dedicated to stack inspection than the lifted state monad--and other monadic evaluators.

scholarly journals Advanced Analytical Treatment of Fractional Logistic Equations Based on Residual Error Functions

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Saleh Alshammari ◽  
Mohammed Al-Smadi ◽  
Mohammad Al Shammari ◽  
Ishak Hashim ◽  
Mohd Almie Alias
Keyword(s):  
Error Function ◽  
High Accuracy ◽  
Residual Error ◽  
Numerical Comparison ◽  
Analytical Treatment ◽  
Suggested Approach ◽  
Error Functions ◽  
Logistic Equations ◽  
Computational Effect ◽  
Solution Methodology

In this article, an analytical reliable treatment based on the concept of residual error functions is employed to address the series solution of the differential logistic system in the fractional sense. The proposed technique is a combination of the generalized Taylor series and minimizing the residual error function. The solution methodology depends on the generation of a fractional expansion in an effective convergence formula, as well as on the optimization of truncated errors, Resqjt, through the use of repeated Caputo derivatives without any restrictive assumptions of system nature. To achieve this, some logistic patterns are tested to demonstrate the reliability and applicability of the suggested approach. Numerical comparison depicts that the proposed technique has high accuracy and less computational effect and is more efficient.

Sign in / Sign up

Export Citation Format

Share Document