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  2. Lattice problem - Wikipedia

    en.wikipedia.org/wiki/Lattice_problem

    To solve the γ-approximation version SVP γ for > for the Euclidean norm, the best known approaches are based on using lattice basis reduction. For large ⁠ γ = 2 Ω ( n ) {\displaystyle \gamma =2^{\Omega (n)}} ⁠ , the Lenstra–Lenstra–Lovász (LLL) algorithm can find a solution in time polynomial in the lattice dimension.

  3. LAPACK - Wikipedia

    en.wikipedia.org/wiki/LAPACK

    aaa is a one- to three-letter code describing the actual algorithm implemented in the subroutine, e.g. SV denotes a subroutine to solve linear system, while R denotes a rank-1 update. For example, the subroutine to solve a linear system with a general (non-structured) matrix using real double-precision arithmetic is called DGESV. [2]: "

  4. HiGHS optimization solver - Wikipedia

    en.wikipedia.org/wiki/HiGHS_optimization_solver

    Since then, a C++ API and other language interfaces have been developed, and modelling utilities and other categories of solver have been added. In early‑2022, the GenX and PyPSA open energy system modelling projects endorsed a funding application for the HiGHS solver in an effort to reduce their community reliance on proprietary libraries. [4]

  5. Basic solution (linear programming) - Wikipedia

    en.wikipedia.org/wiki/Basic_solution_(Linear...

    In linear programming, a discipline within applied mathematics, a basic solution is any solution of a linear programming problem satisfying certain specified technical conditions. For a polyhedron P {\displaystyle P} and a vector x ∗ ∈ R n {\displaystyle \mathbf {x} ^{*}\in \mathbb {R} ^{n}} , x ∗ {\displaystyle \mathbf {x} ^{*}} is a ...

  6. VLSM - Wikipedia

    en.wikipedia.org/?title=VLSM&redirect=no

    From an avoided double redirect: This is a redirect from an alternative title or related topic of Variable-length subnet mask, another redirect to the same title.Because double redirects are disallowed, both pages currently point to Classless Inter-Domain Routing#VLSM.

  7. Basic feasible solution - Wikipedia

    en.wikipedia.org/wiki/Basic_feasible_solution

    There are algorithms for solving an LP in weakly-polynomial time, such as the ellipsoid method; however, they usually return optimal solutions that are not basic. However, Given any optimal solution to the LP, it is easy to find an optimal feasible solution that is also basic. [2]: see also "external links" below.

  8. Short integer solution problem - Wikipedia

    en.wikipedia.org/wiki/Short_integer_solution_problem

    Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based cryptography began in 1996 from a seminal work by Miklós Ajtai [ 1 ] who presented a family of one-way functions based on SIS problem.

  9. Biconjugate gradient stabilized method - Wikipedia

    en.wikipedia.org/wiki/Biconjugate_gradient...

    To solve a linear system Ax = b with a preconditioner K = K 1 K 2 ≈ A, preconditioned BiCGSTAB starts with an initial guess x 0 and proceeds as follows: r 0 = b − Ax 0 Choose an arbitrary vector r̂ 0 such that ( r̂ 0 , r 0 ) ≠ 0 , e.g., r̂ 0 = r 0