PCGS Graded Coin Slab
PCGS may refer to: * Parallel communicating grammar systems, grammar systems working on their own string and communicating with other grammars in a system by sending their sequential forms on request. * Preconditioned conjugate gradient square method, a variant of the preconditioned conjugate gradient method – an algorithm for the numerical solution of systems of linear equations whose matrix is symmetric and positive-definite. * Professional Coin Grading Service Professional Coin Grading Service (PCGS) is an American third-party coin grading, authentication, attribution, and encapsulation service founded in 1985. The intent of its seven founding dealers, including the firm's former president David Hall, ...

Grammar Systems Theory
Grammar systems theory is a field of theoretical computer science that studies systems of finite collections of formal grammars generating a formal language. Each grammar works on a string, a so-called ''sequential form'' that represents an environment. Grammar systems can thus be used as a formalization of decentralized or distributed systems of agents in artificial intelligence. Let \mathbb be a simple reactive agent moving on the table and trying not to fall down from the table with two reactions, ''t'' for turning and ''ƒ'' for moving forward. The set of possible behaviors of \mathbb can then be described as formal language : \mathbb=\, where ''ƒ'' can be done maximally ''k'' times and ''t'' can be done maximally ''ℓ'' times considering the dimensions of the table. Let \mathbb be a which generates language \mathbb. The behavior of \mathbb is then described by this grammar. Suppose the \mathbb has a subsumption architecture; each component of this architectu ...
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Preconditioner
In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods. Preconditioning is typically related to reducing a condition number of the problem. The preconditioned problem is then usually solved by an iterative method. Preconditioning for linear systems In linear algebra and numerical analysis, a preconditioner P of a matrix A is a matrix such that P^A has a smaller condition number than A. It is also common to call T=P^ the preconditioner, rather than P, since P itself is rarely explicitly available. In modern preconditioning, the application of T=P^, i.e., multiplication of a column vector, or a block of column vectors, by T=P^, is commonly performed in a matrix-free fashion, i.e., where neither P, nor T=P^ (and often not even A) are explicitly available in a matrix form. Preconditioners are useful in iterative methods to solve a line ...
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Conjugate Gradient
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems. The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it. The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems. Description of the problem addressed by conju ...
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Preconditioned Conjugate Gradient Method
In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems. The conjugate gradient method can also be used to solve unconstrained optimization problems such as energy minimization. It is commonly attributed to Magnus Hestenes and Eduard Stiefel, who programmed it on the Z4, and extensively researched it. The biconjugate gradient method provides a generalization to non-symmetric matrices. Various nonlinear conjugate gradient methods seek minima of nonlinear optimization problems. Description of the problem addressed by conju ...
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