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In mathematics, computer science, and related subjects, an 'algorithm' is an effective method for solving a problem expressed as a finite sequence of instructions. Algorithms are used for calculation, data processing, and many other fields. (In more advanced or abstract settings, the instructions do not necessarily constitute a finite sequence, or even a sequence; see, for example, "nondeterministic algorithm".) Each algorithm is a list of well-defined instructions for completing a task. Starting from an initial state, the instructions describe a computation that proceeds through a well-defined series of successive states, eventually terminating in a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate randomness. [source = Bing Reference]

Verification of algorithm-intensive systems is a long, costly process. Studies show that the majority of flaws in embedded systems are introduced at the specification stage, but are not detected until late in the development process. These flaws are the dominant cause of project delays and a major contributor to engineering costs. For algorithm-intensive systems —including systems with communications, audio, video, imaging, and navigation functions— these delays and costs are exploding as system complexity increases. It doesn't have to be this way. Many designers of algorithm-intensive systems already have the tools they need to get verification under control. Engineers can use these same tools to build system models that help them find and correct problems earlier in the development process. This can not only reduce verification time, but also improves the performance of their designs. In this article, we'll explain three practical approaches to early verification that make this possible. First, let's examine why the current algorithm verification process is inefficient and error-prone. In a typical workflow, designs start with algorithm developers, who pass the design to hardware and software teams using specification documents.

This paper develops a family of multi-pass image resampling algorithms that use one-dimensional filtering stages to achieve high-quality results at low computational cost. Our key insight is to perform a frequency-domain analysis to ensure that very little aliasing occurs at each stage in the multi-pass transform and to insert additional stages where necessary to ensure this. Using one-dimensional resampling enables the use of small resampling kernels, thus producing highly efficient algorithms. We compare our results with other state of the art software and hardware resampling algorithms.

Ralph Johnson presents a pattern language that he and his colleagues are working on in an attempt to solve the hard issues of parallel programming through a set of design patterns: Structural Patterns, Computational Patterns, Parallel Algorithm Strategy Patterns, Implementation Strategy Patterns, and Concurrent Execution Patterns.

Today sees the launch of Visual Studio 2010, at five launch events around the world, as announced by Bob Muglia, Jason Zander and S. Somasegar, and presented live today in Las Vegas.   Visual Studio 2010 includes the official version 2.0 of the F# language. As is our custom on the F# team, we also release a matching MSI and ZIP of F# 2.0 (for use with Visual Studio 2008 and as a standalone compiler on a range of platforms)   Today represents the culmination of 7 years of work on the language at Microsoft Research, and, more recently, the Microsoft Developer Division. I am immensely proud of what we’ve achieved. F# brings a productive functional and object-oriented programming language to .NET, extending the platform to new audiences in technical, algorithmic, data-rich, parallel and explorative domains, and its inclusion in Visual Studio 2010 represents a huge milestone for the language.   To help understand what we’re doing with F#, I’ve listed some of the common questions people have about the language below.  We thank everyone who has been involved in the production of F#, especially the many users who have given us feedback on the language!

One challenge designers face is the need to translate their algorithms into code for use in embedded targets. The task has proven to be long and prone to error. This article examines how the use of high-level design tools and C code generation capabilities improves the design flow by exploring different use cases and how to reduce the amount of embedded technology expertise required to program embedded targets.

F# is ideal for data-rich, concurrent and algorithmic development: "simple code to solve complex problems". F# is a simple and pragmatic programming language combining functional, object-oriented and scripting programming, and supports cross-platform environments including PC, Mac, and Linux. We'll provide the tutorials, resources and tools you’ll need to begin working with F# right away.