PPT-Conjugate Gradient Method for Indefinite Matrices

Conjugate Gradient 1 CG is a numerical method to solve a linear system of equations 2 CG is used when A is Symmetric and Positive definite matrix SPD 3 CG of Hestenes and . Positive de64257nite matrices ar e even bet ter Symmetric matrices A symmetric matrix is one for which A T If a matrix has some special pr operty eg its a Markov matrix its eigenvalues and eigenvectors ar e likely to have special pr operties as we How Yep Take derivative set equal to zero and try to solve for 1 2 2 3 df dx 1 22 2 2 4 2 df dx 0 2 4 2 2 12 32 Closed8722form solution 3 26 brPage 4br CS545 Gradient Descent Chuck Anderson Gradient Descent Parabola Examples in R Finding Mi The min and max of a function. Michael . Sedivy. Daniel . Eiland. Introduction. Given a function F(x), how do we determine the location of a local extreme (min or max value)?. Two standard methods exist :. :. Application to Compressed Sensing and . Other Inverse . Problems. M´ario. A. T. . Figueiredo. Robert . D. . Nowak. Stephen . J. Wright. Background. Previous Algorithms. Interior-point method. . Date: 24 Jan 07. POC: . 2. Overview. Definitions. Delivery Order Contract . Task Order Contract. FAR References. Types of Indefinite Delivery Contracts. Definite–quantity contracts. Requirements Contracts. CG Method. Non-linear CG. Solving Linear System of Equations. Preconditioned CG and Regularization. Outline. Kiss point. x. g. x*. dx. ’. dx _ . g’. Quasi-Newton Condition: . g. ’ . – . g. A . . is a rectangular arrangement of numbers in rows and columns. . Matrix A below has two rows and three columns. The . . of matrix A are 2X3 (two by three; rows then columns). The numbers in the matrix are called . G.Anuradha. Review of previous lecture-. Steepest Descent. Choose the next step so that the function decreases:. For small changes in . x. we can approximate . F. (. x. ):. where. If we want the function to decrease:. What is a matrix?. A Matrix is just rectangular arrays of items. A typical . matrix . is . a rectangular array of numbers arranged in rows and columns.. Sizing a matrix. By convention matrices are “sized” using the number of rows (m) by number of columns (n).. Michael . Sedivy. Daniel . Eiland. Introduction. Given a function F(x), how do we determine the location of a local extreme (min or max value)?. Two standard methods exist :. F(x) with global minimum D and local minima B and F. Shi & Bo. What is sparse system. A system of linear equations is called sparse if . only a relatively small . number of . its matrix . elements . . are nonzero. It is wasteful to use general methods . A cofactor matrix . C. of a matrix . A. is the square matrix of the same order as . A. in which each element a. ij. is replaced by its cofactor c. ij. . . Example:. If. The cofactor C of A is. Matrices - Operations. Rotation of coordinates -the rotation matrixStokes Parameters and unpolarizedlight1916 -20041819 -1903Hans Mueller1900 -1965yyxyEEEElinear arbitrary anglepolarization right or left circularpolarizati This Slideshow was developed to accompany the textbook. Precalculus. By Richard Wright. https://www.andrews.edu/~rwright/Precalculus-RLW/Text/TOC.html. Some examples and diagrams are taken from the textbook..