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  2. Hypersurface - Wikipedia

    en.wikipedia.org/wiki/Hypersurface

    In geometry, a hypersurface is a generalization of the concepts of hyperplane, plane curve, and surface.A hypersurface is a manifold or an algebraic variety of dimension n − 1, which is embedded in an ambient space of dimension n, generally a Euclidean space, an affine space or a projective space. [1]

  3. Decision boundary - Wikipedia

    en.wikipedia.org/wiki/Decision_boundary

    In a statistical-classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other side as belonging ...

  4. Level set - Wikipedia

    en.wikipedia.org/wiki/Level_set

    When n = 3, a level set is called a level surface (or isosurface); so a level surface is the set of all real-valued roots of an equation in three variables x 1, x 2 and x 3. For higher values of n, the level set is a level hypersurface, the set of all real-valued roots of an equation in n > 3 variables. A level set is a special case of a fiber.

  5. Euclidean algorithm - Wikipedia

    en.wikipedia.org/wiki/Euclidean_algorithm

    The Euclidean algorithm was probably invented before Euclid, depicted here holding a compass in a painting of about 1474. The Euclidean algorithm is one of the oldest algorithms in common use. [27] It appears in Euclid's Elements (c. 300 BC), specifically in Book 7 (Propositions 1–2) and Book 10 (Propositions 2–3). In Book 7, the algorithm ...

  6. Hyperplane - Wikipedia

    en.wikipedia.org/wiki/Hyperplane

    In geometry, a hyperplane of an n-dimensional space V is a subspace of dimension n − 1, or equivalently, of codimension 1 in V.The space V may be a Euclidean space or more generally an affine space, or a vector space or a projective space, and the notion of hyperplane varies correspondingly since the definition of subspace differs in these settings; in all cases however, any hyperplane can ...

  7. List of unsolved problems in computer science - Wikipedia

    en.wikipedia.org/wiki/List_of_unsolved_problems...

    What is the fastest algorithm for matrix multiplication? Can all-pairs shortest paths be computed in strongly sub-cubic time, that is, in time O(V 3−ϵ) for some ϵ>0? Can the Schwartz–Zippel lemma for polynomial identity testing be derandomized? Does linear programming admit a strongly polynomial-time algorithm?

  8. Smallest-circle problem - Wikipedia

    en.wikipedia.org/wiki/Smallest-circle_problem

    The dual to this quadratic program may also be formulated explicitly; [17] an algorithm of Lawson [18] can be described in this way as a primal dual algorithm. [ 16 ] Shamos and Hoey [ 7 ] proposed an O( n log n ) time algorithm for the problem based on the observation that the center of the smallest enclosing circle must be a vertex of the ...

  9. Bitonic tour - Wikipedia

    en.wikipedia.org/wiki/Bitonic_tour

    It is a standard exercise in dynamic programming to devise a polynomial time algorithm that constructs the optimal bitonic tour. [ 1 ] [ 2 ] Although the usual method for solving it in this way takes time O ( n 2 ) {\displaystyle O(n^{2})} , a faster algorithm with time O ( n log 2 ⁡ n ) {\displaystyle O(n\log ^{2}n)} is known.