Fast, modern algorithms
The latest algorithms developed around the world and in-house at Wolfram Research are built into
Mathematica functions, along with the automation to invoke them when appropriate.
Systemwide adaptive scalability
Numerical or graphical algorithms have to sample points to evaluate functions. Sample too many and you sacrifice performance; too few and you get inaccurate results. Unlike most other systems,
Mathematica automatically adapts the sampling rate to the function's behavior at each stage in a calculation, optimizing performance for a given algorithm.
High-Impact Adaptive Visualization
Just-in-time compilation
Mathematica automatically applies its internal compiler to optimize numerical computations when this can improve total start-to-finish time. The process is transparent: you get higher performance without changing your input.
Optimized array handling
Different forms of arrays (
e.g., sparse, machine-precision number, etc.) are represented internally in a variety of ways to optimize processing speed and memory usage. The full set of
Mathematica commands are available for working with all forms of arrays.
Autovectorizing
Mathematica applies operations automatically to an entire vector, matrix, or array rather than just a single element--enhancing performance and ease-of-use.
Hardware-optimized numerical performance
Mathematica is consistently the first-to-market technical software with complete implementation for new hardware, OSes, and chipsets, often beating other systems by months or years. Ports are individually optimized to give you the best performance for your platform.
Mathematica is one of the first applications to support 64-bit computing.
Every Mathematica is multicore
Parallel computation and automatic control is included with every
Mathematica--making the most of your multicore computer to speed up built-in capabilities as well as your own functions.
Parallelize across the grid
With gridMathematica, parallelize not only your numerical computations, but symbolic too.
gridMathematica is a powerful parallel technical-computing system that delivers the world's largest collection of algorithms.
Self-checking precision control
Mathematica verifies and controls the precision of numerical calculations as it performs them, ensuring much greater consistency of results than previously possible. You have the choice to specify input, output, or working precision;
Mathematica will give outputs corresponding to the justifiable precision.
Minimized start-to-finish time
Rather than purely optimizing computational performance,
Mathematica cuts down total start-to-finish time through integrating all stages in the workflow from high-level symbolic problem specification through prototyping to simulation, reliability analysis, and deployment of results.
Hybrid symbolics-numerics
By preprocessing your numerical problems with symbolic techniques,
Mathematica can increase computational performance, improve reliability, and cover a broader scope.
Always use the best algorithm
Mathematica consistently matches the best performing algorithm to your problem both because it contains a broad range of algorithms, and because
Mathematica automates and optimizes selection between algorithms (even mid-calculation). Systemwide automatic algorithm selection is unique to
Mathematica and eliminates a major source of poor speed and reliability performance in other systems.
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