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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
Conjugate_gradient_method
Algorithm for solving matrix-vector equations
In numerical linear algebra, the conjugate gradient squared method (CGS) is an iterative algorithm for solving systems of linear equations of the form
Conjugate gradient squared method
Conjugate_gradient_squared_method
Concept in mathematics
biconjugate gradient method (BiCG) and has faster and smoother convergence than the original BiCG as well as other variants such as the conjugate gradient squared
Biconjugate gradient stabilized method
Biconjugate_gradient_stabilized_method
Algorithm for solving systems of linear equations
biconjugate gradient method is an algorithm to solve systems of linear equations A x = b . {\displaystyle Ax=b.\,} Unlike the conjugate gradient method, this
Biconjugate_gradient_method
Optimization algorithm
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate
Gradient_descent
Mathematical optimization method
iterates. This method, and modifications, are globally convergent under mild conditions, and perform competitively with conjugate gradient methods for many
Barzilai–Borwein_method
Numerical approximation algorithm
method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of an iterative method or a method of
Iterative_method
Optimization algorithm
Quasi-Newton methods for optimization are based on Newton's method to find the stationary points of a function, points where the gradient is 0. Newton's method assumes
Quasi-Newton_method
Study of mathematical algorithms for optimization problems
Polyak, subgradient–projection methods are similar to conjugate–gradient methods. Bundle method of descent: An iterative method for small–medium-sized problems
Mathematical_optimization
Algorithm used to solve non-linear least squares problems
LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in
Levenberg–Marquardt_algorithm
Algorithm for finding zeros of functions
Newton's method did not converge Aitken's delta-squared process Bisection method Euler method Fast inverse square root Fisher scoring Gradient descent
Newton's_method
Model-free reinforcement learning algorithm
algorithm for training an intelligent agent. Specifically, it is a policy gradient method, often used for deep RL when the policy network is very large. The
Proximal_policy_optimization
Visualization method
iterative methods of solving ill-posed inverse problems, such as the Landweber algorithm, Modified Richardson iteration and Conjugate gradient method. "L-Curve
L-curve
Discontinued online library
solutions methods are: Richardson Iteration Chebyshev Iteration Conjugate Gradient (CG) Conjugate Gradient Squared (CGS) BiConjugate Gradient (BiCG) BiConjugate
IML++
Solving an optimization problem with a quadratic objective function
problems a variety of methods are commonly used, including interior point, active set, augmented Lagrangian, conjugate gradient, gradient projection, extensions
Quadratic_programming
Topics referred to by the same term
Isogonal conjugate, in geometry Conjugate gradient method, an algorithm for the numerical solution of particular systems of linear equations Conjugate points
Conjugation
Algorithm for linear programming
cycling Criss-cross algorithm Cutting-plane method Devex algorithm Fourier–Motzkin elimination Gradient descent Karmarkar's algorithm Nelder–Mead simplicial
Simplex_algorithm
Concept in mathematics
setting is known as Online Mirror Descent (OMD). Gradient descent Multiplicative weight update method Hedge algorithm Bregman divergence Arkadi Nemirovsky
Mirror_descent
Mathematical term
Nonlinear conjugate gradient method, generalizes the conjugate gradient method to nonlinear optimization Stochastic gradient descent, iterative method for optimizing
Slope
Numerical method for solving physical or engineering problems
is symmetric and positive definite, so a technique such as the conjugate gradient method is favored. For problems that are not too large, sparse LU decompositions
Finite_element_method
Topics referred to by the same term
forms on request. Preconditioned conjugate gradient square method, a variant of the preconditioned conjugate gradient method – an algorithm for the numerical
PCGS
Computer optimization methods
Proximal gradient (forward backward splitting) methods for learning is an area of research in optimization and statistical learning theory which studies
Proximal gradient methods for learning
Proximal_gradient_methods_for_learning
Approximation method in statistics
zig-zag trajectory towards the minimum. Conjugate gradient search. This is an improved steepest descent based method with good theoretical convergence properties
Non-linear_least_squares
Statistical algorithm
least mean square of the error signal (difference between the desired and the actual signal). It is a stochastic gradient descent method in that the
Least_mean_squares_filter
Method of data analysis
advanced matrix-free methods, such as the Lanczos algorithm or the Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG) method. Subsequent principal
Principal_component_analysis
Algorithm
cost than other iterative methods, such as the conjugate gradient method. In 2009, a randomized version of the Kaczmarz method for overdetermined linear
Kaczmarz_method
Matrix decomposition method
positive-definite matrix into the product of a lower triangular matrix and its conjugate transpose, which is useful for efficient numerical solutions, e.g., Monte
Cholesky_decomposition
Field of engineering
equation Newton's method Steepest descent Conjugate gradient Sequential quadratic programming Hooke-Jeeves pattern search Nelder-Mead method Genetic algorithm
Multidisciplinary design optimization
Multidisciplinary_design_optimization
Overview of and topical guide to statistics
Semidefinite programming Newton-Raphson Gradient descent Conjugate gradient method Mirror descent Proximal gradient method Geometric programming List of statistical
Outline_of_statistics
Methods for numerical approximations
usually used as though they were not, e.g. GMRES and the conjugate gradient method. For these methods the number of steps needed to obtain the exact solution
Numerical_analysis
Method to solve optimization problems
Linear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical
Linear_programming
Mathematical algorithm
non-linear least squares problems, which is equivalent to minimizing a sum of squared function values. It is an extension of Newton's method for finding a
Gauss–Newton_algorithm
Transforms equations for numerical solution
preconditioned iterative methods for linear systems include the preconditioned conjugate gradient method, the biconjugate gradient method, and generalized minimal
Preconditioner
Overview of and topical guide to deep learning
Backpropagation Conjugate gradient method Generalized Hebbian algorithm Gradient descent Levenberg–Marquardt algorithm Perceptron Quasi-Newton method Wake-sleep
Outline_of_deep_learning
iteration Conjugate gradient method (CG) — assumes that the matrix is positive definite Derivation of the conjugate gradient method Nonlinear conjugate gradient
List of numerical analysis topics
List_of_numerical_analysis_topics
Method of estimating the parameters of a statistical model
This is the case when conjugate priors are used. Via numerical optimization such as the conjugate gradient method or Newton's method. This usually requires
Maximum a posteriori estimation
Maximum_a_posteriori_estimation
Iterative optimisation algorithm
Powell's dog leg method, also called Powell's hybrid method, is an iterative optimisation algorithm for the solution of non-linear least squares problems, introduced
Powell's_dog_leg_method
Iterative method used to solve a linear system of equations
end end end Conjugate gradient method Gaussian belief propagation Iterative method: Linear systems Kaczmarz method (a "row-oriented" method, whereas Gauss-Seidel
Gauss–Seidel_method
Partitioning a digital image into segments
Extracted features are accurately reconstructed using an iterative conjugate gradient matrix method. In one kind of segmentation, the user outlines the region
Image_segmentation
Technique in analytical chemistry
PMID 16460742. S2CID 26072994. Dolan, John W. (2014). "LC Method Scaling, Part II: Gradient Separations". LCGC North America. 32 (3): 188–193. Martin
High-performance liquid chromatography
High-performance_liquid_chromatography
Property of a mathematical matrix
generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number z ∗ M z {\displaystyle
Definite_matrix
Array of numbers
solving linear systems Ax = b for sparse matrices A, such as the conjugate gradient method. An algorithm is, roughly speaking, numerically stable if little
Matrix_(mathematics)
Subfield of mathematical optimization
Duality Karush–Kuhn–Tucker conditions Optimization problem Proximal gradient method Algorithmic problems on convex sets Nesterov & Nemirovskii 1994 Murty
Convex_optimization
Solving multiple machine learning tasks at the same time
discovery and data mining. Ji, S., & Ye, J. (2009). An accelerated gradient method for trace norm minimization. Proceedings of the 26th Annual International
Multi-task_learning
Solution process for some optimization problems
the current point; First-order routines - use also the values of the gradients of these functions; Second-order routines - use also the values of the
Nonlinear_programming
Problem optimization method
programming (DP) is both a mathematical optimization method and an algorithmic paradigm. The method was developed by Richard Bellman in the 1950s and has
Dynamic_programming
Representation learning method
After applying one of the optimization methods to the value of the dual (such as Newton's method or conjugate gradient) we get the value of D {\displaystyle
Sparse_dictionary_learning
Signal processing technique
are then solved with the conjugate gradient least squares method and the simple gradient descent method respectively. The method is stopped when the desired
Compressed_sensing
Subfield of convex optimization
solved by interior point methods. All linear programs and (convex) quadratic programs can be expressed as SDPs, and the sum of squares hierarchy of SDPs can
Semidefinite_programming
Concept in convex optimization mathematics
differentiable, subgradient methods for unconstrained problems use the same search direction as the method of gradient descent. Subgradient methods are slower than
Subgradient_method
Mathematical optimization problem restricted to integers
the branch and bound method. For example, the branch and cut method that combines both branch and bound and cutting plane methods. Branch and bound algorithms
Integer_programming
{\displaystyle A} , followed by the use of an iterative solver such as conjugate gradient descent. One of the benefits of this algorithm is that the number
Neighbourhood components analysis
Neighbourhood_components_analysis
Scientific instruments
amplitude control of phase-only computer generated holograms using conjugate gradient minimisation". Optics Express. 25 (10): 11692–11700. arXiv:1701.08620
Optical_tweezers
Type of visual artifact
on gradient echo‐based T2‐weighted sequences. B1 inhomogeneity has been successfully mitigated by adjusting coil type and configurations. One method is
MRI_artifact
Optimizing objective functions that have constrained variables
constrained case, often via the use of a penalty method. However, search steps taken by the unconstrained method may be unacceptable for the constrained problem
Constrained_optimization
Signal processing system
found here: Least Mean Squares Algorithm Sample Matrix Inversion Algorithm Recursive Least Square Algorithm Conjugate gradient method Constant Modulus Algorithm
Adaptive_beamformer
Term in mathematical optimization
reasonable approximation. Trust-region methods are in some sense dual to line-search methods: trust-region methods first choose a step size (the size of
Trust_region
an actual box, not a placeholder) Denotes the d'Alembertian or squared four-gradient, which is a generalization of the Laplacian to four-dimensional
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Chemical added to show pH of a solution
for the basic form and "Ind+" for the conjugate acid of the indicator. The ratio of concentration of conjugate acid/base to concentration of the acidic/basic
PH_indicator
systems of linear equations Biconjugate gradient method: solves systems of linear equations Conjugate gradient: an algorithm for the numerical solution
List_of_algorithms
Type of mathematical function
2014-07-14. Michael J. D. Powell (1977). "Restart procedures for the conjugate gradient method". Mathematical Programming. 12 (1): 241–254. doi:10.1007/bf01593790
Radial_basis_function
Java library for linear algebra
the Templates project: BiConjugate gradients. BiConjugate gradients stabilized. Conjugate gradients. Conjugate gradients squared. Chebyshev iteration. Generalized
Matrix_Toolkit_Java
Approximation of a matrix's Cholesky factorization
factorization is often used as a preconditioner for algorithms like the conjugate gradient method. The Cholesky factorization of a positive definite matrix A of
Incomplete Cholesky factorization
Incomplete_Cholesky_factorization
Gauss-Newton. Many different methods exist (e.g. BFGS, conjugate gradient, stochastic gradient) but as steepest gradient and Gauss-Newton are the only
YaDICs
Evolutionary algorithm
scenario, where gradients are not available (or not useful) and function evaluations are the only considered cost of search, the CMA-ES method is likely to
CMA-ES
Machine learning and applied statistics
the method of conjugate gradients, Nordsieck methods, Gaussian quadrature rules, and quasi-Newton methods. In all these cases, the classic method is based
Probabilistic_numerics
Specialized notation for multivariable calculus
many derivatives in an organized way. As a first example, consider the gradient from vector calculus. For a scalar function of three independent variables
Matrix_calculus
Numerical eigenvalue calculation
The Lanczos algorithm is an iterative method devised by Cornelius Lanczos that is an adaptation of power methods to find the m {\displaystyle m} "most
Lanczos_algorithm
Quantum physics-based metaheuristic for optimization problems
Sebenik, C.; Stenson, C.; Doll, J. D. (1994). "Quantum annealing: A new method for minimizing multidimensional functions". Chemical Physics Letters. 219
Quantum_annealing
In mathematics, invariant of square matrices
determinant of the complex conjugate of a complex matrix (which is also the determinant of its conjugate transpose) is the complex conjugate of its determinant
Determinant
Statistical model for a binary dependent variable
linear regression. There, the sum of the squared deviations of the fit from the data points (yk), the squared error loss, is taken as a measure of the
Logistic_regression
Chernoff's distribution Chernoff's inequality Chi distribution Chi-squared distribution Chi-squared test Chinese restaurant process Choropleth map Chow test Chronux
List_of_statistics_articles
Estimation method that minimizes the mean square error
decomposition, while for large sparse systems conjugate gradient method is more effective. Levinson recursion is a fast method when C Y {\displaystyle C_{Y}} is also
Minimum mean square error estimator
Minimum_mean_square_error_estimator
Unit hypercube of variable dimension whose corners have been perturbed
Bland, Robert G. (May 1977). "New finite pivoting rules for the simplex method". Mathematics of Operations Research. 2 (2): 103–107. doi:10.1287/moor.2
Klee–Minty_cube
Topics referred to by the same term
International Dose-Response Society, published by SAGE Nonlinear conjugate gradient method, an algorithm for numerically finding the minimum of a nonlinear
Nonlinearity_(disambiguation)
Class of algorithms that find approximate solutions to optimization problems
algorithmic techniques for these formulations are applied. Rounding-based methods. This involves solving the considered formulation for a good fractional
Approximation_algorithm
that S is convex, it is minimized when its gradient vector is zero (This follows by definition: if the gradient vector is not zero, there is a direction
Proofs involving ordinary least squares
Proofs_involving_ordinary_least_squares
Gradient pattern analysis (GPA) is a geometric computing method for characterizing geometrical bilateral symmetry breaking of an ensemble of symmetric
Gradient_pattern_analysis
Technique for finding an extremum of a function
relative error in x {\displaystyle x} is approximately proportional to the squared absolute error in f ( x ) {\displaystyle f(x)} in typical cases. For that
Golden-section_search
Branch of physics
vector during conjugate gradient iterations. The method of moments (MoM) or boundary element method (BEM) is a numerical computational method of solving
Computational electromagnetics
Computational_electromagnetics
Linear programming algorithm
algorithm that solves these problems in polynomial time. The ellipsoid method is also polynomial time but proved to be inefficient in practice. Denoting
Karmarkar's_algorithm
Decomposition of periodic functions
})} is the conjugate symmetric function S R E + i S I O . {\displaystyle S_{\mathrm {RE} }+i\ S_{\mathrm {IO} }.} Conversely, a conjugate symmetric transform
Fourier_series
Force distributed over an area
every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume. It is defined as a derivative of the internal energy of a system:
Pressure
published 2001 – LOBPCG Locally Optimal Block Preconditioned Conjugate Gradient method finding extreme eigenvalues of symmetric eigenvalue problems by
Timeline_of_algorithms
Iterative method for solving the Sylvester matrix equations
example use of the conjugate gradient method preconditioned with incomplete Cholesky factorization). The idea behind the ADI method is to split the finite
Alternating-direction implicit method
Alternating-direction_implicit_method
computation of the global minimum. Interior/Direct algorithm Interior/Conjugate Gradient algorithm Active Set algorithm Sequential Quadratic Programming (SQP)
Artelys_Knitro
Measure of difference between two points
Bregman distance is the squared Euclidean distance D F ( x , y ) = ‖ x − y ‖ 2 {\displaystyle D_{F}(x,y)=\|x-y\|^{2}} . The squared Mahalanobis distance
Bregman_divergence
Matrix manipulation algorithm
example, in the preconditioned conjugate gradient algorithm.) Minimum degree algorithms are often used in the finite element method where the reordering of nodes
Minimum_degree_algorithm
Figure formed by two rays meeting at a common point
straight angle is termed the supplement of the angle. Explementary angles or conjugate angles sum to a full angle (1 turn, 360°, or 2π radians). The difference
Angle
Device to reflect radiation back to its source
systems such as high-power lasers and optical transmission lines. Phase-conjugate mirrors reflect an incoming wave so that the reflected wave exactly follows
Retroreflector
Type of energy transfer
defined through changes in the system’s macroscopic state variables, in conjugate pairs such as pressure and volume, or magnetisation and magnetic field
Heat
Metaheuristic proposed by Xin-She Yang
the other hand, has little to distinguish it from PSO, with the inverse-square law having a similar effect to crowding and fitness sharing in EAs, and
Firefly_algorithm
Statistical concept
distribution (the conjugate prior of the categorical distribution), and the parameters will be distributed according to their respective conjugate priors. Mathematically
Mixture_model
Field of mathematics
linear problem Ax = b, the classical iterative approach is the conjugate gradient method. If A is not symmetric, then examples of iterative solutions to
Numerical_linear_algebra
Criterion for model selection
)=-\ln(p(x\mid \theta ,M)\pi (\theta \mid M))/n} . If the sequence of gradients { ∇ ℓ n ( θ ) } {\displaystyle \{\nabla \ell _{n}(\theta )\}} is Lipschitz
Bayesian information criterion
Bayesian_information_criterion
Number, approximately 3.14
classical Poisson kernel associated with a Brownian motion in a half-plane. Conjugate harmonic functions and so also the Hilbert transform are associated with
Pi
Chinese scientist and revolutionary (born 1961)
Autonomous Federation. He was a prominent student leader at the Tiananmen Square protests of 1989. Liu holds an M.A. in physics from Peking University and
Liu_Gang
Second-order partial differential equation
divergence operator (also symbolized "div"), ∇ {\displaystyle \nabla } is the gradient operator (also symbolized "grad"), and f ( x , y , z ) {\displaystyle f(x
Laplace's_equation
Formulation of classical mechanics
canonically conjugate to the original variables. For example, given a set of generalized coordinates, the variables canonically conjugate are the generalized
Lagrangian_mechanics
Function related to statistics and probability theory
probability distribution of the test statistic is approximately a chi-squared distribution with degrees-of-freedom (df) equal to the difference in df's
Likelihood_function
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
Boy/Male
Arabic, Muslim
Scared
Girl/Female
Hindu
Scared
Girl/Female
Muslim
Scared
Surname or Lastname
English
English : patronymic from Squire.
Boy/Male
English American
Shieldbearer.
Boy/Male
British, English
Great
Boy/Male
Hindu, Indian
Scared
Boy/Male
Hindu, Indian, Marathi
Scared
Girl/Female
Hindu
Equaled, Similar
Surname or Lastname
Swedish
Swedish : unexplained.German : unexplained.English : unexplained.
Boy/Male
American, Australian, British, English
Shield Bearer; Knight's Companion
Surname or Lastname
English
English : status name from Middle English squyer ‘esquire’, ‘a man belonging to the feudal rank immediately below that of knight’ (from Old French esquier ‘shield bearer’). At first it denoted a young man of good birth attendant on a knight, or by extension any attendant or servant, but by the 14th century the meaning had been generalized, and referred to social status rather than age. By the 17th century, the term denoted any member of the landed gentry, but this is unlikely to have influenced the development of the surname.
Girl/Female
Tamil
Equaled, Similar
Girl/Female
Latin
Grace.
Boy/Male
French Latin
A squire.
Male
French
French form of Roman Latin Gratian, GRATIEN means "pleasing, agreeable."
Boy/Male
American, British, English
Gray-haired; Son of the Gray Family; Son of Gregory
Girl/Female
Tamil
Scared
Boy/Male
Italian
Squire.
Boy/Male
Tamil
Harshnil | ஹரà¯à®·à¯à®¨à¯€à®²
Scared
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
Boy/Male
Tamil
Umaiyavan | உமையவாந
Lord Shiva
Girl/Female
English
Means light or most beautiful woman.
Female
German
 Low German form of German Irma, IMMA means "entire, whole." Compare with another form of Imma.
Girl/Female
Tamil
Dharshaneeya | தரà¯à®·à®¾à®¨à¯‡à®¯à®¾Â
Boy/Male
Celtic Gaelic American
From the gray fortress.
Male
Egyptian
, the praenomen of king Ergamenes.
Girl/Female
Tamil
Lord Vishnu
Girl/Female
Tamil
Chitrathi | சிதà¯à®°à®¤à¯€
A bright chariot
Boy/Male
Hindu, Indian, Punjabi, Sikh
One in whom Peace Prevades
Boy/Male
Tamil
Chinmayananda | சிநà¯à®®à®¯à®¾à®¨à®‚தாÂ
Blissful, Supreme consciousness
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
CONJUGATE GRADIENT-SQUARED-METHOD
a.
Rising or descending by regular degrees of inclination; as, the gradient line of a railroad.
n.
One who squares, or quarrels; a hot-headed, contentious fellow.
n.
Hence, anything which is square, or nearly so
n.
The rate of increase or decrease of a variable magnitude, or the curve which represents it; as, a thermometric gradient.
imp. & p. p.
of Squire
a.
Having the two things that are conjugate parts of the same figure; as, self-conjugate triangles.
n.
An instrument having at least one right angle and two or more straight edges, used to lay out or test square work. It is of several forms, as the T square, the carpenter's square, the try-square., etc.
n.
Alt. of Gradine
p. pr. & vb. n.
of Conjugate
a.
Of or pertaining to a square, or to squares; resembling a quadrate, or square; square.
imp. & p. p.
of Conjugate
imp. & p. p.
of Square
a.
Beaming with vivacity and happiness; as, a radiant face.
a.
Giving off rays; -- said of a bearing; as, the sun radiant; a crown radiant.
n.
A square piece or fragment.
v. t.
To form or shape into wrinkles or folds, or alternate ridges and grooves, as by drawing, contraction, pressure, bending, or otherwise; to wrinkle; to purse up; as, to corrugate plates of iron; to corrugate the forehead.
n.
One who, or that which, squares.
a.
Moving by steps; walking; as, gradient automata.
a.
Forming a right angle; as, a square corner.
a.
Rendering equal justice; exact; fair; honest, as square dealing.