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Everything about Conjugate gradient method
Mathematical optimization algorithm
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-semidefinite. 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. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: Conjugate gradient methodA 5-minute orientation
- Skim a recent paper: Accelerated computing of dynamic carbon emission factor for large-scale power grid using conjugate gradient squared method with p-norm preconditionerInfluential work since 2022
- Pick up a classic book: Neuro-fuzzy and soft computingThe most-reprinted book on the subject
- Read the landmark paper: A generalized conjugate gradient, least square methodCited 137 times
- Go sideways: Biconjugate gradient methodA closely related topic
- Go sideways: Anderson accelerationA closely related topic
đź“– Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
- Description of the problem addressed by conjugate gradients
- Derivation as a direct method
- As an iterative method
- Finite Termination Property
- Convergence properties
- The preconditioned conjugate gradient method
- The flexible preconditioned conjugate gradient method
- Vs. the locally optimal steepest descent method
- Conjugate gradient method as optimal feedback controller for double integrator
- Conjugate gradient on the normal equations
- Conjugate gradient method for complex Hermitian matrices
- Advantages and disadvantages
🏆 Landmark papers (most cited)
A generalized conjugate gradient, least square method
Extended conjugate gradient squared and conjugate residual squared methods for solving the generalized coupled Sylvester tensor equations
Formulation of a Preconditioned Algorithm for the Conjugate Gradient Squared Method in Accordance with Its Logical Structure
Preconditioned tensor format conjugate gradient squared and biconjugate gradient stabilized methods for solving stein tensor equations
Conjugate gradient squared algorithm for panel methods
Changing over stopping criterion for stable solving nonsymmetric linear equations by preconditioned conjugate gradient squared method
🆕 Influential since 2022
đź“š Books worth reading
Neuro-fuzzy and soft computingJyh-Shing Roger Jang, Chuen-Tsai Sun · 1996
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
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