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In some applications, the sampling of the data is generally not related to the geometry of the manifold we are interested in describing. In this case, we can set = and the diffusion operator approximates the Laplace–Beltrami operator. We then recover the Riemannian geometry of the data set regardless of the distribution of the points.
In applied mathematics, test functions, known as artificial landscapes, are useful to evaluate characteristics of optimization algorithms, such as convergence rate, precision, robustness and general performance.
ProximalOperators.jl: a Julia package implementing proximal operators. ProximalAlgorithms.jl: a Julia package implementing algorithms based on the proximal operator, including the proximal gradient method. Proximity Operator repository: a collection of proximity operators implemented in Matlab and Python
The most common source inputs for high-level synthesis are based on standard languages such as ANSI C/C++, SystemC and MATLAB. High-level synthesis typically also includes a bit-accurate executable specification as input, since to derive an efficient hardware implementation, additional information is needed on what is an acceptable Mean-Square ...
Commentary is introduced into regular scripts by the characters || and continue to the end of the same line. An alternative commenting convention affects an entire source code file, known as a "literate script", in which every line is considered a comment unless it starts with a > sign. Miranda's basic data types are char, num and bool.
If the operator was self-adjoint, =, the direct state equation and the adjoint state equation would have the same left-hand side. In the goal of never inverting a matrix, which is a very slow process numerically, a LU decomposition can be used instead to solve the state equation, in O ( m 3 ) {\displaystyle O(m^{3})} operations for the ...
In computer science, an operator-precedence parser is a bottom-up parser that interprets an operator-precedence grammar.For example, most calculators use operator-precedence parsers to convert from the human-readable infix notation relying on order of operations to a format that is optimized for evaluation such as Reverse Polish notation (RPN).
Modern implementations for Boolean operations on polygons tend to use plane sweep algorithms (or Sweep line algorithms). A list of papers using plane sweep algorithms for Boolean operations on polygons can be found in References below. Boolean operations on convex polygons and monotone polygons of the same direction may be performed in linear ...