Norm Of The Error
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Vector, such as the solution x of a linear system Ax=b, Matrix, such as a matrix inverse , and Subspace, such as the space spanned by one or more eigenvectors of a matrix. This section provides measures for errors in
Norm Error Matlab
these quantities, which we need in order to express error bounds. First, consider scalars. Let l2 error norm the scalar be an approximation of the true answer . We can measure the difference between and either by the absolute error , or, relative norms definition if is nonzero, by the relative error . Alternatively, it is sometimes more convenient to use instead of the standard expression for relative error. If the relative error of is, say, , we say that is accurate to 5 decimal
L2 Relative Error Norm
digits. To measure the error in vectors, we need to measure the size or norm of a vector x. A popular norm is the magnitude of the largest component, , which we denote by . This is read the infinity norm of x. See Table6.2 for a summary of norms. Table 6.2: Vector and matrix norms If is an approximation to the exact vector x, we will refer to as the absolute error in (where p
L2 Norm Error Matlab
is one of the values in Table6.2) and refer to as the relative error in (assuming ). As with scalars, we will sometimes use for the relative error. As above, if the relative error of is, say , we say that is accurate to 5 decimal digits. The following example illustrates these ideas. Thus, we would say that approximates x to 2 decimal digits. Errors in matrices may also be measured with norms. The most obvious generalization of to matrices would appear to be , but this does not have certain important mathematical properties that make deriving error bounds convenient. Instead, we will use , where A is an m-by-n matrix, or ; see Table6.2 for other matrix norms. As before, is the absolute error in , is the relative error in , and a relative error in of means is accurate to 5 decimal digits. The following example illustrates these ideas. so is accurate to 1 decimal digit. We now introduce some related notation we will use in our error bounds. The condition number of a matrix A is defined as , where A is square and invertible, and p is or one of the other possibilities in Table6.2. The condition number measures how sensitive is to changes in A; the larger the condition number, the more sensitive is . For example, for the same A as in the last example, ScaLAPACK error estimat
Support Support Newsreader MathWorks Search MathWorks.com MathWorks Newsreader Support MATLAB Newsgroup MATLAB Central Community Home MATLAB Answers File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Post relative error between two vectors A New Message Advanced Search Help MATLAB Central Community Home MATLAB Answers
2 Norm Condition Number Of A Matrix
File Exchange Cody Blogs Newsreader Link Exchange ThingSpeak Anniversary Home Post A New Message Advanced Search Help Trial row sum norm calculator software Norm of the error Subject: Norm of the error From: Richard Date: 30 Mar, 2006 09:08:00 Message: 1 of 4 Reply to this message Add author to My Watch List http://netlib.org/scalapack/slug/node135.html View original format Flag as spam Good day All! I need to write a function to evaluate "the norm of the error" between measured and predicted outputs. This function is to be used in MATLAB's fminsearch to find various response parameters. Question: Does anyone know how to find the norm of the error using these two datasets? I'm not looking for a https://www.mathworks.com/matlabcentral/newsreader/view_thread/120815 MATLAB function, rather the actual procedure itself. I've googled on "norm of error" etc, and it is mentioned often but I can't find any actual step-by-step guides for how to find the norm of the error. Any ideas welcome! Cheers4now Richard Subject: Norm of the error From: vijitnair@gmail.com Date: 30 Mar, 2006 06:22:05 Message: 2 of 4 Reply to this message Add author to My Watch List View original format Flag as spam I guess you are looking for an objective function to be used in fminsearch. there are more than a few choices mean square error sum of squared errors mean absolute error normalized error chi-square error The choice is dictated by the kind of data set you have. Sum of squared residuals/least squares is the most popular but it is also very susceptible to noise. This might help http://www.itl.nist.gov/div898/handbook/pmd/section1/pmd14.htm Subject: Norm of the error From: joa Date: 30 Mar, 2006 18:16:21 Message: 3 of 4 Reply to this message Add author to My Watch List View original format Flag as spam Believe it or not, it's called 'norm' :-) For vect
consists of computing, at each node: the difference the relative difference the percentage where is the exact solution and is the calculated solution, and printing, for each https://www.rocq.inria.fr/modulef/Doc/GB/Guide6-10/node21.html degree of freedom: the error norm the relative error norm the relative error norm the maximum error by indicating in addition the number and coordinates of the node where the maximum occurs. Preprocessor NORMXX compares the calculated solution with the exact solution for those cases where the solution to a problem is known analytically. It calls module NORME: SUBROUTINE NORME (M,XM,DM,NFMAIL,NIMAIL,NFCOOR,NICOOR,NFB,NIB, + NFBS,NIBS,INDICB,NSM,FONINT,SOLEX,DSOLEX) C norm error ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C AIM : IPRINT THE EXACT SOLUTION, THE CALCULATED SOLUTION, C --- THE ABSOLUTE AND RELATIVE DIFFERENCES BETWEEN THEM, C THE L1,L2 ERRORS AND MAX C ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ where M, XM and DM designates the super array, NFMAIL, NIMAIL are the file number and level of structure MAIL, NFCOOR, NICOOR are the file number and level of structure COOR, NFB, NIB are the file norm error matlab number and level of structure B, NFBS, NIBS are the file number and level of structure B on exit, INDICB is the save option: 1 : the error is stored in NFBS (used in this case), 0 if not, NSM is the number of the load case to consider (between 1 and NDSM), FONINT is a logical set to .TRUE. if functions SOLEX or DSOLEX are input as interpreted functions, and set to .FALSE. if they are input in the classical manner, SOLEX, DSOLEX are the functions used to input the exact solution (in single or double precision). Depending on the value of FONINT, functions SOLEX or DSOLEX must be written using the following format: FUNCTION SOLEX(I,X,Y,Z) DOUBLE PRECISION FUNCTION DSOLEX(I,X,Y,Z) where I is the degree of freedom number of the node with coordinates X, Y and Z. 2.10.2 Norm corresponding to D.S. TAE Preprocessor NORMXX compares the calculated stresses with the exact solution for those cases where the stresses of elasticity problem is known analytically, using the same method of computation as for a D.S. B as seen above. It calls module NORTAE: SUBROUTINE NORTAE(M,XM,DM,NFTAE,NITAE,NFTAES,NITAES,INDICB, + FONINT,SOLEX,DSOLEX,NSM,NC1) C ++++++++++++++++++++++
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