L2 Norm Of The Error

Random Entry New in MathWorld MathWorld Classroom About MathWorld Contribute to MathWorld Send a Message to the Team MathWorld Book Wolfram Web Resources» 13,594 entries Last updated: Wed Oct 19 2016 Created, euclidean norm of a matrix developed, and nurturedbyEricWeisstein at WolframResearch Calculus and Analysis>Norms> History and Terminology>Notation> 2 norm of a vector Interactive Entries>Interactive Demonstrations> L^2-Norm The -norm (also written "-norm") is a vector norm defined for a complex vector l2 norm matlab (1) by (2) where on the right denotes the complex modulus. The -norm is the vector norm that is commonly encountered in vector algebra and vector operations (such as

L1 Norm Vs L2 Norm

the dot product), where it is commonly denoted . However, if desired, a more explicit (but more cumbersome) notation can be used to emphasize the distinction between the vector norm and complex modulus together with the fact that the -norm is just one of several possible types of norms. For real vectors, the absolute value sign indicating that l2 norm numpy a complex modulus is being taken on the right of equation (2) may be dropped. So, for example, the -norm of the vector is given by (3) The -norm is also known as the Euclidean norm. However, this terminology is not recommended since it may cause confusion with the Frobenius norm (a matrix norm) is also sometimes called the Euclidean norm. The -norm of a vector is implemented in the Wolfram Language as Norm[m, 2], or more simply as Norm[m]. The "-norm" (denoted with an uppercase ) is reserved for application with a function , (4) with denoting an angle bracket. SEE ALSO: Angle Bracket, Complete Set of Functions, L1-Norm, L2-Space, L-infty-Norm, Parallelogram Law, Vector Norm REFERENCES: Gradshteyn, I.S. and Ryzhik, I.M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, pp.1114-1125, 2000. Horn, R.A. and Johnson, C.R. "Norms for Vectors and Matrices." Ch.5 in Matrix Analysis. Cambridge, England: Cambridge University Press, 1990. CITE THIS AS: Weisstein, Eric W. "L^2-Norm." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/L2-Norm.html Wolfram We

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 degree of freedom: euclidean-norm example the error norm the relative error norm the relative error norm the maximum

Norm Of A Vector Example

error by indicating in addition the number and coordinates of the node where the maximum occurs. Preprocessor NORMXX compares the

L2 Norm Regularization

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 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C AIM : IPRINT http://mathworld.wolfram.com/L2-Norm.html 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 number and level of structure B, NFBS, NIBS https://www.rocq.inria.fr/modulef/Doc/GB/Guide6-10/node21.html 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 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ C AIM : PRINT THE EXACT SOLUTION THE CALCULATED SOLUTION, C --- THE ABSOLUTE AND RELATIVE

tour help Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site About Us Learn more about Stack Overflow the company Business Learn more about hiring developers or posting ads with http://scicomp.stackexchange.com/questions/2822/what-norm-to-choose-when us Computational Science beta Questions Tags Users Badges Unanswered Ask Question _ Computational Science Stack Exchange is http://www.cfd-online.com/Forums/main/123353-l0-l1-l2-linf-error-norms.html a question and answer site for scientists using computers to solve scientific problems. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What norm to choose when? up vote 7 down vote favorite 2 Recently, I saw this question: how to measure the error 2 norm of a finite difference method I am student of simulation sciences and unfortunately, for me, it's totally unclear, what norm to use in what context. Quite often, we use the Euclidian norm or the L2 norm, but why does one choose different norms, what's their meaning besides the numerical / mathematical definition? Or more precise: What is the reason to use a specific norm in a specific context? error-estimation share|improve this question edited Jul 16 '12 at 8:03 asked Jul 15 '12 at 12:25 norm of a vanCompute 414316 2 This is a huge question. Are you interested in norms for measuring errors in numerical solutions of differential equations? If so, you should narrow the scope of the question. –David Ketcheson Jul 15 '12 at 12:51 At the moment, we are calculating the solutions of simple PDEs like the Poisson equation. But my question is not focused on that. I want to learn, how to use norms in general. –vanCompute Jul 15 '12 at 13:04 2 From the FAQ: Your questions should be reasonably scoped. If you can imagine an entire book that answers your question, you’re asking too much. –David Ketcheson Jul 15 '12 at 14:58 My problem is, that I cannot even image an antire book with the answer to that question. It's somehow a missing piece/gap in my knowledge. The answer to that problem can't be that big, as everybody uses norms. If you see the chance of narrowing the question to make it more precise, than I am open to that. I will reformulate the question a bit, I hope it is better then. –vanCompute Jul 16 '12 at 8:02 There are many. Here's one: books.google.co.uk/books/about/… –David Ketcheson Jul 16 '12 at 9:00 | show 1 more comment 3 Answers 3 active oldest votes up vote 10 down vote accepted For measuring the error in the solution of PDE, it is quite natural to choose the norm of the space in which the solution lies. Fo

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