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The demands of accuracy in measurements and engineering models today, renders the condition number of problems larger. While a corresponding increase in the precision of floating point numbers ensured a stable computing, the uncertainty in…
Fixed-parameter algorithms have been successfully applied to solve numerous difficult problems within acceptable time bounds on large inputs. However, most fixed-parameter algorithms are inherently \emph{sequential} and, thus, make no use…
This paper considers the problem of channel coding with a given (possibly suboptimal) maximum-metric decoding rule. A cost-constrained random-coding ensemble with multiple auxiliary costs is introduced, and is shown to achieve error…
The computing industry is forced to find alternative design approaches and computing platforms to sustain increased power efficiency, while providing sufficient performance. Among the examined solutions, Approximate Computing, Hardware…
Iterative Closest Point (ICP) is a widely used method for performing scan-matching and registration. Being simple and robust method, it is still computationally expensive and may be challenging to use in real-time applications with limited…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…
It is well known that the computation of accurate trajectories of the Lorenz system is a difficult problem. Computed solutions are very sensitive to the discretization error determined by the time step size and polynomial order of the…
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…
Since numbers in the computer are represented with a fixed number of bits, loss of accuracy during calculation is unavoidable. At high precision where more bits (e.g. 64) are allocated to each number, round-off errors are typically small.…
With the help of special program package PAREVAL designed in {\sl Mathematica} system we reproduce values of basic fundamental physical constants obtained by NIST and recommended by CODATA for international usage since 1998. In our…
The post-Moore era casts a shadow of uncertainty on many aspects of computer system design. Managing that uncertainty requires new algorithmic tools to make quantitative assessments. While prior uncertainty quantification methods, such as…
Given a set $F$ of $n$ positive functions over a ground set $X$, we consider the problem of computing $x^*$ that minimizes the expression $\sum_{f\in F}f(x)$, over $x\in X$. A typical application is \emph{shape fitting}, where we wish to…
Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…
Stochastic rounding (SR) is a probabilistic method used to round numbers to floating-point and fixed-point representations. In length $n$ summation, the worst-case error of SR grows as $\sqrt{n}$ with high probability, unlike for standard…
To well understand the behavior of quantum error correction codes (QECC) in noise processes, we need to obtain explicit coding maps for QECC. Due to extraordinary amount of computational labor that they entails, explicit coding maps are a…
We provide tools to help automate the error analysis of algorithms that evaluate simple functions over the floating-point numbers. The aim is to obtain tight relative error bounds for these algorithms, expressed as a function of the unit…
Coherent network error correction is the error-control problem in network coding with the knowledge of the network codes at the source and sink nodes. With respect to a given set of local encoding kernels defining a linear network code, we…
Entanglement-assisted quantum error-correcting codes (EAQECCs) to desired rate, error-correcting capability and maximum shared entanglement are constructed. Thus for a required rate $R$, required error-correcting capability to correct $t$…