enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Tridiagonal matrix algorithm - Wikipedia

    en.wikipedia.org/wiki/Tridiagonal_matrix_algorithm

    In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations. A tridiagonal system for n unknowns may be written as

  3. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    The conjugate gradient method with a trivial modification is extendable to solving, given complex-valued matrix A and vector b, the system of linear equations = for the complex-valued vector x, where A is Hermitian (i.e., A' = A) and positive-definite matrix, and the symbol ' denotes the conjugate transpose.

  4. Newton's method - Wikipedia

    en.wikipedia.org/wiki/Newton's_method

    One may also use Newton's method to solve systems of k equations, which amounts to finding the (simultaneous) zeroes of k continuously differentiable functions :. This is equivalent to finding the zeroes of a single vector-valued function F : R k → R k . {\displaystyle F:\mathbb {R} ^{k}\to \mathbb {R} ^{k}.}

  5. System of linear equations - Wikipedia

    en.wikipedia.org/wiki/System_of_linear_equations

    The simplest method for solving a system of linear equations is to repeatedly eliminate variables. This method can be described as follows: In the first equation, solve for one of the variables in terms of the others. Substitute this expression into the remaining equations. This yields a system of equations with one fewer equation and unknown.

  6. Quasi-Newton method - Wikipedia

    en.wikipedia.org/wiki/Quasi-Newton_method

    More recently quasi-Newton methods have been applied to find the solution of multiple coupled systems of equations (e.g. fluid–structure interaction problems or interaction problems in physics). They allow the solution to be found by solving each constituent system separately (which is simpler than the global system) in a cyclic, iterative ...

  7. Alternating-direction implicit method - Wikipedia

    en.wikipedia.org/wiki/Alternating-direction...

    In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations.It is a popular method for solving the large matrix equations that arise in systems theory and control, [1] and can be formulated to construct solutions in a memory-efficient, factored form.

  8. Generalized minimal residual method - Wikipedia

    en.wikipedia.org/wiki/Generalized_minimal...

    In mathematics, the generalized minimal residual method (GMRES) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. The method approximates the solution by the vector in a Krylov subspace with minimal residual. The Arnoldi iteration is used to find this vector.

  9. Dormand–Prince method - Wikipedia

    en.wikipedia.org/wiki/Dormand–Prince_method

    Dormand–Prince is the default method in the ode45 solver for MATLAB [4] and GNU Octave [5] and is the default choice for the Simulink's model explorer solver. It is an option in Python's SciPy ODE integration library [6] and in Julia's ODE solvers library. [7] Implementations for the languages Fortran, [8] Java, [9] and C++ [10] are also ...