dl = A in .NET

Build qr codes in .NET dl = A
dl = A
Qr Codes generation on .net
use .net vs 2010 qr-code creator tomake qrcode on .net
IIAt Tol12
Visual .net denso qr bar code reader with .net
Using Barcode recognizer for visual .net Control to read, scan read, scan image in visual .net applications.
IIA dll12
Barcode development with .net
generate, create barcode none for .net projects
(2.5.89b) (2.5.89c) (2.5.89d)
scan bar code for .net
Using Barcode decoder for .NET Control to read, scan read, scan image in .NET applications.
= Xo + (tld l = TO - (XlAd l
Control qr bidimensional barcode data in c#.net
qr bidimensional barcode data in c#.net
and for i = 2,3, ...
Create qr code iso/iec18004 on .net
using barcode writer for asp.net aspx control to generate, create qr-codes image in asp.net aspx applications.
(2.5.90a)
Control qr code iso/iec18004 image on vb
use .net vs 2010 qr code iso/iec18004 creation toinclude qr codes with visual basic.net
(2.5.90b)
.net Vs 2010 2d matrix barcode encoder with .net
use visual studio .net 2d barcode creator tobuild 2d matrix barcode in .net
(2.5.90c)
Get ansi/aim code 39 for .net
use .net vs 2010 barcode 3 of 9 generation toadd code-39 in .net
= Xi-l + (Xidi = Ti-l - (Xi A di
PDF-417 2d Barcode barcode library for .net
using visual .net crystal toencode pdf 417 for asp.net web,windows application
(2.5.90d)
Create barcode on .net
using vs .net toassign barcode on asp.net web,windows application
(2.5.90e)
USS-93 encoder in .net
use .net crystal code 93 full ascii integrating tocreate ansi/aim code 93 with .net
Let A be a real matrix, then there exist orthogonal matrices of U and V and diagonal matrix ~ such that
GS1 - 13 creation with .net
using report rdlc toattach upc - 13 on asp.net web,windows application
_ ===t A=U~V
Control gs1 - 13 image for microsoft word
use word ean13+5 generating tocreate ean13+5 on word
(2.5.91 )
Bar Code generating with .net
generate, create bar code none for .net projects
5.3 General Real Matrix and Complex Matrix
GTIN - 13 maker with microsoft excel
using microsoft excel tobuild gs1 - 13 on asp.net web,windows application
where
Word Documents barcode creation in word documents
use office word bar code printing toprint bar code with office word
= diag(a1' a2,'"
Control pdf417 size on java
pdf-417 2d barcode size with java
,an)
Barcode barcode library for java
using java topaint barcode on asp.net web,windows application
a1 ~ a2 ~ ... ~ an ~
EAN128 integrated on vb.net
use .net windows forms crystal ucc - 12 encoding toreceive ean 128 barcode on visual basic
(2.5.92)
This is known as singular value decomposition. Using the L 2 norm for vectors, let the matrix norm be
(2.5.93)
The relations between matrix norm and singular values are
(2.5.94)
Since
--1 ---l-t
the largest singular value of A =-1
(2.5.95)
is 1/an .
(2.5.96)
The condition number is
(2.5.97)
If the condition number is large, the matrix solution can be unstable. To change the condition number, pre-conditioning can be done. Let
(2.5.98)
The goal is to find a pre-conditioning matrix C
x'=Cx --1 x=C X'
Then ==-1 _ AC X' = b =-1 Multiply by C =-1==-1 I =-1_ C AC X = C b Let
(2.5.99) (2.5.100)
(2.5.101)
(2.5.102)
--1---1
A =C
(2.5.103) (2.5.104)
=-1_ b = C b
2 INTEGRAL EQUATION FORMULATIONS AND NUMERICAL METHODS
Then
Ax' =b
-, -
(2.5.105)
A judicious choice of the pre-conditioning matrix can drastically change the condition number. To make the computation of A efficient, C and C be simple matrices. must
REFERENCES
REFERENCES AND ADDITIONAL READINGS
Anderson, M. G. (1965), Scattering from bodies of revolution, IEEE Trans. Antennas Propagat., 13, 303-310. Barrett, R., M. Berry, T. F. Chan, J. Dammel, J. Donato, J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst (1993), Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM Publications, Philadelphia, PA. Borup, D. T. and O. P. Gandhi (1985), Calculation of high resolution SAR distributions in biological bodies using the FFT algorithm and conjugate gradient method, IEEE Trans. Microwave Theory Tech., 33, 417-419. Brigham, E. O. (1988), The Fast Fourier Transform and its Applications, Prientice-Hall, Englewood Cliffs, NJ. Catedra, M. F., E. Gago, and L. Nuno (1989), A numerical scheme to obtain the RCS of three-dimensional bodies of resonant size using the conjugate gradient method and the fast Fourier transform, IEEE Trans. Antennas Propagat., 37, 528-537. Chan, C. H. and R. Mittra (1987), Some recent developments in iterative techniques for solving electromagnetic boundary value problems, Radio Sci., 22(6), 929-934. Chew, W. C. (1990), Waves and Fields in Inhomogeneous Media, Van Nostrand Reinhold, New York. Gan, H. and W. C. Chew (1995), A discrete BCG-FFT algorithm for solving 3D inhomogeneous scatterer problems, J. Electromag. Waves and Appl., 9, 1339-1357. Glisson, A. W. and D. R. Wilton (1979), Simple and efficient numerical techniques for treating bodies of revolution, Technical Report 105, Engineering Experiment Station, The University of Mississippi, University, Mississippi. Glisson, A. W. and D. R. Wilton (1980), Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces, IEEE Trans. Antennas Propagat., 28, 593-603. Goedecke, G. H. and S. G. O'Brien (1988), Scattering by irregular inhomogeneous particles via the digitized Green's function algorithm, Appl. Optics, 27, 2431-2438. Golub, G. H. and C. F. Van Loan (1996), Matrix Computations, 3rd edition, Johns Hopkins University Press, Baltimore, MD. Goodman, J. J., B. T. Drain, and P. J. Flatau (1991), Application of fast-Fourier-transform techniques to the discrete-dipole approximation, Optics Lett., 16(15), 1198-1200. Gradshteyn,1. S. and 1. M. Ryzhik (1965), Table of Integrals, Series and Products, Academic Press, New York. Harrington, R. F. (1968), Field Computation by Moment Method, Macmillan, New York. Hestenes, M. R. and E. Stiefel (1952), Methods of conjugate gradients for solving linear systems, J. Res. Nat. Bur. Standards, 49, 409-436. Jackson, J. D. (1975), Classical Electrodynamics, John Wiley & Sons, New York. Jin, J. M. and J. L. Volakis (1992), A biconjugate gradient FFT solution for scattering by planar plates, Electromagnetics, 12, 105-109. Joseph, J. (1990), Application of integral equation and finite difference method to electromagnetic scattering by two dimensional and boy of revolution geometries, Ph.D. thesis, Department of Electrical Engineering and Computer Science, University of UrbanaChampaign, Urbana, IL. Kas, A. and E. L. Yip (1987), Preconditioned conjugate gradient methods for solving electromagnetic problems, IEEE Trans. Antennas Propagat., 35,147-152.