162,696 research outputs found
High accuracy computation with linear analog optical systems: a critical study
High accuracy optical processors based on the algorithm of digital multiplication by analog convolution (DMAC) are studied for ultimate performance limitations. Variations of optical processors that perform high accuracy vector-vector inner products are studied in abstract and with specific examples. It is concluded that the use of linear analog optical processors in performing digital computations with DMAC leads to impractical requirements for the accuracy of analog optical systems and the complexity of postprocessing electronics
Improved Accuracy and Parallelism for MRRR-based Eigensolvers -- A Mixed Precision Approach
The real symmetric tridiagonal eigenproblem is of outstanding importance in
numerical computations; it arises frequently as part of eigensolvers for
standard and generalized dense Hermitian eigenproblems that are based on a
reduction to tridiagonal form. For its solution, the algorithm of Multiple
Relatively Robust Representations (MRRR) is among the fastest methods. Although
fast, the solvers based on MRRR do not deliver the same accuracy as competing
methods like Divide & Conquer or the QR algorithm. In this paper, we
demonstrate that the use of mixed precisions leads to improved accuracy of
MRRR-based eigensolvers with limited or no performance penalty. As a result, we
obtain eigensolvers that are not only equally or more accurate than the best
available methods, but also -in most circumstances- faster and more scalable
than the competition
FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search
We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for
\textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search
system for ultra-high dimensional datasets on a single machine, that does not
require similarity computations and is tailored for high-performance computing
platforms. By leveraging a LSH style randomized indexing procedure and
combining it with several principled techniques, such as reservoir sampling,
recent advances in one-pass minwise hashing, and count based estimations, we
reduce the computational and parallelization costs of similarity search, while
retaining sound theoretical guarantees.
We evaluate FLASH on several real, high-dimensional datasets from different
domains, including text, malicious URL, click-through prediction, social
networks, etc. Our experiments shed new light on the difficulties associated
with datasets having several million dimensions. Current state-of-the-art
implementations either fail on the presented scale or are orders of magnitude
slower than FLASH. FLASH is capable of computing an approximate k-NN graph,
from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than
10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam
dataset, using brute-force (), will require at least 20 teraflops. We
provide CPU and GPU implementations of FLASH for replicability of our results
Mira: A Framework for Static Performance Analysis
The performance model of an application can pro- vide understanding about its
runtime behavior on particular hardware. Such information can be analyzed by
developers for performance tuning. However, model building and analyzing is
frequently ignored during software development until perfor- mance problems
arise because they require significant expertise and can involve many
time-consuming application runs. In this paper, we propose a fast, accurate,
flexible and user-friendly tool, Mira, for generating performance models by
applying static program analysis, targeting scientific applications running on
supercomputers. We parse both the source code and binary to estimate
performance attributes with better accuracy than considering just source or
just binary code. Because our analysis is static, the target program does not
need to be executed on the target architecture, which enables users to perform
analysis on available machines instead of conducting expensive exper- iments on
potentially expensive resources. Moreover, statically generated models enable
performance prediction on non-existent or unavailable architectures. In
addition to flexibility, because model generation time is significantly reduced
compared to dynamic analysis approaches, our method is suitable for rapid
application performance analysis and improvement. We present several scientific
application validation results to demonstrate the current capabilities of our
approach on small benchmarks and a mini application
- …