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  2. 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.

  3. DIDO (software) - Wikipedia

    en.wikipedia.org/wiki/DIDO_(software)

    The MATLAB/DIDO toolbox does not require a "guess" to run the algorithm. This and other distinguishing features have made DIDO a popular tool to solve optimal control problems. [4] [7] [15] The MATLAB optimal control toolbox has been used to solve problems in aerospace, [11] robotics [1] and search theory. [2]

  4. Conjugate residual method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_residual_method

    The conjugate residual method is an iterative numeric method used for solving systems of linear equations. It's a Krylov subspace method very similar to the much more popular conjugate gradient method, with similar construction and convergence properties. This method is used to solve linear equations of the form

  5. Biconjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Biconjugate_gradient_method

    In mathematics, more specifically in numerical linear algebra, the biconjugate gradient method is an algorithm to solve systems of linear equations A x = b . {\displaystyle Ax=b.\,} Unlike the conjugate gradient method , this algorithm does not require the matrix A {\displaystyle A} to be self-adjoint , but instead one needs to perform ...

  6. 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

  7. Biconjugate gradient stabilized method - Wikipedia

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

    Preconditioners are usually used to accelerate convergence of iterative methods. 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; ρ 0 ...

  8. Proximal gradient method - Wikipedia

    en.wikipedia.org/wiki/Proximal_gradient_method

    Proximal gradient methods are a generalized form of projection used to solve non-differentiable convex optimization problems. A comparison between the iterates of the projected gradient method (in red) and the Frank-Wolfe method (in green). Many interesting problems can be formulated as convex optimization problems of the form

  9. Adjoint state method - Wikipedia

    en.wikipedia.org/wiki/Adjoint_state_method

    The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...