From non-linear least squares to weighted linear least squares The 2019 Stack Overflow Developer Survey Results Are InJacobi-Method with Projection onto Box ConstraintMoore-Penrose Inverse as least-squares solutionLinear Least Squares with Linear Equality Constraints - Iterative SolverLeast Squares Algorithm with Inverse NormLinear least squares in $mathbbR^3$ with three data points.Sensitivity of weighted least squares estimation methodLinear Least SquaresWeighted Least Squares for Parabola Coefficients EstimationLeast squares method to a square system of equations that has a unique solutionleast-squares problem $|Ahatx-b|_2 = min_x|Ax-b|_2$

Why isn't airport relocation done gradually?

How come people say “Would of”?

Return to UK after being refused

Are there any other methods to apply to solving simultaneous equations?

What is the use of option -o in the useradd command?

Unbreakable Formation vs. Cry of the Carnarium

Why is the maximum length of OpenWrt’s root password 8 characters?

Understanding the implication of what "well-defined" means for the operation in quotient group

Inflated grade on resume at previous job, might former employer tell new employer?

What could be the right powersource for 15 seconds lifespan disposable giant chainsaw?

Where does the "burst of radiance" from Holy Weapon originate?

I see my dog run

How do you say "canon" as in "official for a story universe"?

A poker game description that does not feel gimmicky

How to deal with fear of taking dependencies

Limit to 0 ambiguity

Inline version of a function returns different value than non-inline version

Could a US political party gain complete control over the government by removing checks & balances?

When to use the root test. Is this not a good situation to use it?

Lethal sonic weapons

Why is it "Tumoren" and not "Tumore"?

What is the best strategy for white in this position?

Spanish for "widget"

What can other administrators access on my machine?



From non-linear least squares to weighted linear least squares



The 2019 Stack Overflow Developer Survey Results Are InJacobi-Method with Projection onto Box ConstraintMoore-Penrose Inverse as least-squares solutionLinear Least Squares with Linear Equality Constraints - Iterative SolverLeast Squares Algorithm with Inverse NormLinear least squares in $mathbbR^3$ with three data points.Sensitivity of weighted least squares estimation methodLinear Least SquaresWeighted Least Squares for Parabola Coefficients EstimationLeast squares method to a square system of equations that has a unique solutionleast-squares problem $|Ahatx-b|_2 = min_x|Ax-b|_2$










1












$begingroup$


Given an overdetermined linear system $A in mathbbR^m times n$, $b in mathbbR^m times 1$. And a non-linear function $f(x)$. Given a non-linear least squares:
$$ e^* = min_g leftlVert f(A g) - brightrVert_2^2,$$
where the function $f(x)$ is applied element-wise. What would be the best weight $W$ depending on $b$ for a weighted linear least squares
$$
hate = min_g leftlVert W A g - W brightrVert_2^2,
$$

such that $min$.










share|cite|improve this question











$endgroup$
















    1












    $begingroup$


    Given an overdetermined linear system $A in mathbbR^m times n$, $b in mathbbR^m times 1$. And a non-linear function $f(x)$. Given a non-linear least squares:
    $$ e^* = min_g leftlVert f(A g) - brightrVert_2^2,$$
    where the function $f(x)$ is applied element-wise. What would be the best weight $W$ depending on $b$ for a weighted linear least squares
    $$
    hate = min_g leftlVert W A g - W brightrVert_2^2,
    $$

    such that $min$.










    share|cite|improve this question











    $endgroup$














      1












      1








      1





      $begingroup$


      Given an overdetermined linear system $A in mathbbR^m times n$, $b in mathbbR^m times 1$. And a non-linear function $f(x)$. Given a non-linear least squares:
      $$ e^* = min_g leftlVert f(A g) - brightrVert_2^2,$$
      where the function $f(x)$ is applied element-wise. What would be the best weight $W$ depending on $b$ for a weighted linear least squares
      $$
      hate = min_g leftlVert W A g - W brightrVert_2^2,
      $$

      such that $min$.










      share|cite|improve this question











      $endgroup$




      Given an overdetermined linear system $A in mathbbR^m times n$, $b in mathbbR^m times 1$. And a non-linear function $f(x)$. Given a non-linear least squares:
      $$ e^* = min_g leftlVert f(A g) - brightrVert_2^2,$$
      where the function $f(x)$ is applied element-wise. What would be the best weight $W$ depending on $b$ for a weighted linear least squares
      $$
      hate = min_g leftlVert W A g - W brightrVert_2^2,
      $$

      such that $min$.







      calculus optimization least-squares weighted-least-squares






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Mar 30 at 12:54







      Sebastian Schlecht

















      asked Mar 30 at 12:27









      Sebastian SchlechtSebastian Schlecht

      24918




      24918




















          0






          active

          oldest

          votes












          Your Answer





          StackExchange.ifUsing("editor", function ()
          return StackExchange.using("mathjaxEditing", function ()
          StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
          StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
          );
          );
          , "mathjax-editing");

          StackExchange.ready(function()
          var channelOptions =
          tags: "".split(" "),
          id: "69"
          ;
          initTagRenderer("".split(" "), "".split(" "), channelOptions);

          StackExchange.using("externalEditor", function()
          // Have to fire editor after snippets, if snippets enabled
          if (StackExchange.settings.snippets.snippetsEnabled)
          StackExchange.using("snippets", function()
          createEditor();
          );

          else
          createEditor();

          );

          function createEditor()
          StackExchange.prepareEditor(
          heartbeatType: 'answer',
          autoActivateHeartbeat: false,
          convertImagesToLinks: true,
          noModals: true,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          imageUploader:
          brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
          contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
          allowUrls: true
          ,
          noCode: true, onDemand: true,
          discardSelector: ".discard-answer"
          ,immediatelyShowMarkdownHelp:true
          );



          );













          draft saved

          draft discarded


















          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168249%2ffrom-non-linear-least-squares-to-weighted-linear-least-squares%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown

























          0






          active

          oldest

          votes








          0






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















          draft saved

          draft discarded
















































          Thanks for contributing an answer to Mathematics Stack Exchange!


          • Please be sure to answer the question. Provide details and share your research!

          But avoid


          • Asking for help, clarification, or responding to other answers.

          • Making statements based on opinion; back them up with references or personal experience.

          Use MathJax to format equations. MathJax reference.


          To learn more, see our tips on writing great answers.




          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3168249%2ffrom-non-linear-least-squares-to-weighted-linear-least-squares%23new-answer', 'question_page');

          );

          Post as a guest















          Required, but never shown





















































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown

































          Required, but never shown














          Required, but never shown












          Required, but never shown







          Required, but never shown







          Popular posts from this blog

          Triangular numbers and gcdProving sum of a set is $0 pmod n$ if $n$ is odd, or $fracn2 pmod n$ if $n$ is even?Is greatest common divisor of two numbers really their smallest linear combination?GCD, LCM RelationshipProve a set of nonnegative integers with greatest common divisor 1 and closed under addition has all but finite many nonnegative integers.all pairs of a and b in an equation containing gcdTriangular Numbers Modulo $k$ - Hit All Values?Understanding the Existence and Uniqueness of the GCDGCD and LCM with logical symbolsThe greatest common divisor of two positive integers less than 100 is equal to 3. Their least common multiple is twelve times one of the integers.Suppose that for all integers $x$, $x|a$ and $x|b$ if and only if $x|c$. Then $c = gcd(a,b)$Which is the gcd of 2 numbers which are multiplied and the result is 600000?

          Ingelân Ynhâld Etymology | Geografy | Skiednis | Polityk en bestjoer | Ekonomy | Demografy | Kultuer | Klimaat | Sjoch ek | Keppelings om utens | Boarnen, noaten en referinsjes Navigaasjemenuwww.gov.ukOffisjele webside fan it regear fan it Feriene KeninkrykOffisjele webside fan it Britske FerkearsburoNederlânsktalige ynformaasje fan it Britske FerkearsburoOffisjele webside fan English Heritage, de organisaasje dy't him ynset foar it behâld fan it Ingelske kultuergoedYnwennertallen fan alle Britske stêden út 'e folkstelling fan 2011Notes en References, op dizze sideEngland

          Հադիս Բովանդակություն Անվանում և նշանակություն | Դասակարգում | Աղբյուրներ | Նավարկման ցանկ