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Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
We revisit the problem of computing with noisy information considered in Feige et al. 1994, which includes computing the OR function from noisy queries, and computing the MAX, SEARCH and SORT functions from noisy pairwise comparisons. For…
An important question in evolutionary computation is how good solutions evolutionary algorithms can produce. This paper aims to provide an analytic analysis of solution quality in terms of the relative approximation error, which is defined…
Software methods introduced for automated design of approximate implementations of arithmetic circuits rely on fast and accurate evaluation of approximate candidate implementations. To accelerate the evaluation of circuit error, we propose…
Interval arithmetic is hardly feasible without directed rounding as provided, for example, by the IEEE floating-point standard. Equally essential for interval methods is directed rounding for conversion between the external decimal and…
In the classical selection problem, the input consists of a collection of elements and the goal is to pick a subset of elements from the collection such that some objective function $f$ is maximized. This problem has been studied…
Providing feedback on programming assignments is a tedious task for the instructor, and even impossible in large Massive Open Online Courses with thousands of students. Previous research has suggested that program repair techniques can be…
Techniques that rigorously bound the overall rounding error exhibited by a numerical program are of significant interest for communities developing numerical software. However, there are few available tools today that can be used to…
Stochastic optimization often involves calculating the expected value of a first-order max or min function, known as a first-order loss function. In this context, loss functions are frequently approximated using piecewise linear functions.…
The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and…
A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is…
Programming is increasingly taught using block-based languages like Scratch. While the use of blocks prevents syntax errors, learners can still make semantic mistakes, requiring feedback and help. As teachers may be overwhelmed by help…
A selection of algorithms for the rational approximation of matrix-valued functions are discussed, including variants of the interpolatory AAA method, the RKFIT method based on approximate least squares fitting, vector fitting, and a method…
The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…
Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…
In courses that involve programming assignments, giving meaningful feedback to students is an important challenge. Human beings can give useful feedback by manually grading the programs but this is a time-consuming, labor intensive, and…
Hybrid automata are a natural framework for modeling and analyzing systems which exhibit a mixed discrete continuous behaviour. However, the standard operational semantics defined over such models implicitly assume perfect knowledge of the…
We present a new algorithm for computing upper bounds on the number of executions of each program instruction during any single program run. The upper bounds are expressed as functions of program input values. The algorithm is primarily…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
We explore the use of expert iteration in the context of language modeling applied to formal mathematics. We show that at same compute budget, expert iteration, by which we mean proof search interleaved with learning, dramatically…