Gradient methods | Numerical linear algebra

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. (Wikipedia).

Conjugate gradient method
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From playlist Advanced Calculus / Multivariable Calculus

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From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables

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From playlist Calculus 3

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From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables

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This video explains how to find the gradient of a function of two variables. The meaning of the gradient is explained and shown graphically. Site: http://mathispower4u.com

From playlist The Chain Rule and Directional Derivatives, and the Gradient of Functions of Two Variables

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From playlist Advanced Calculus / Multivariable Calculus

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Download the free PDF http://tinyurl.com/EngMathYT A basic tutorial on the gradient field of a function. We show how to compute the gradient; its geometric significance; and how it is used when computing the directional derivative. The gradient is a basic property of vector calculus. NOT

From playlist Engineering Mathematics

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From playlist Vector Calculus for Engineers

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From playlist [Coursera] Neural Networks for Machine Learning — Geoffrey Hinton

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From playlist Neural Networks for Machine Learning by Professor Geoffrey Hinton [Complete]

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From playlist Statistical Physics of Machine Learning 2020

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From playlist MIT 18.086 Mathematical Methods for Engineers II, Spring '06

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From playlist Functions of Several Variables - Calculus

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Residual (numerical analysis) | Gram–Schmidt process | Krylov subspace | MATLAB | Mathematical optimization | Jacobi method | Biconjugate gradient method | Double integrator | Conjugate residual method | Nonlinear conjugate gradient method | Conjugate transpose | Condition number | GNU Octave | Conjugate gradient method | Polynomial ring | Gauss–Seidel method | Arnoldi iteration | Sparse matrix–vector multiplication | Iterative method | Cholesky decomposition | Double-precision floating-point format | Energy minimization | System of linear equations | Mathematics | Belief propagation | Quadratic function | Spectrum of a matrix | Optimal control | Real number | Preconditioner | Gradient descent | Sparse matrix | Hessian matrix | Symmetric matrix | Basis (linear algebra) | Round-off error | Incomplete Cholesky factorization | Line search | Transpose | Inner product space | Partial differential equation | Algorithm