Trapezoidal least squares system

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











up vote
0
down vote

favorite












I want to solve a least squares problem
$$
A x = b
$$
where $A$ is a $m times n$ lower trapezoidal matrix (zero above the diagonal), $x$ is $n times 1$, $b$ is $m times 1$, and $m > n$. So $A$ has the structure
$$
A = pmatrixL \ K
$$
where $L$ is $n times n$ lower triangular, and $K$ is $(m-n) times n$ and dense.



I can't find a LAPACK or BLAS routine to call to solve this. Can this system be solved efficiently without needing to perform a QR or SVD on the matrix $A$? $A$ is already in $LQ$ form so I'm hoping this can be taken advantage of somehow.






linear-algebra least-squares







share|cite|improve this question



























    up vote
    0
    down vote

    favorite












    I want to solve a least squares problem
    $$
    A x = b
    $$
    where $A$ is a $m times n$ lower trapezoidal matrix (zero above the diagonal), $x$ is $n times 1$, $b$ is $m times 1$, and $m > n$. So $A$ has the structure
    $$
    A = pmatrixL \ K
    $$
    where $L$ is $n times n$ lower triangular, and $K$ is $(m-n) times n$ and dense.



    I can't find a LAPACK or BLAS routine to call to solve this. Can this system be solved efficiently without needing to perform a QR or SVD on the matrix $A$? $A$ is already in $LQ$ form so I'm hoping this can be taken advantage of somehow.






    linear-algebra least-squares







    share|cite|improve this question

























      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I want to solve a least squares problem
      $$
      A x = b
      $$
      where $A$ is a $m times n$ lower trapezoidal matrix (zero above the diagonal), $x$ is $n times 1$, $b$ is $m times 1$, and $m > n$. So $A$ has the structure
      $$
      A = pmatrixL \ K
      $$
      where $L$ is $n times n$ lower triangular, and $K$ is $(m-n) times n$ and dense.



      I can't find a LAPACK or BLAS routine to call to solve this. Can this system be solved efficiently without needing to perform a QR or SVD on the matrix $A$? $A$ is already in $LQ$ form so I'm hoping this can be taken advantage of somehow.






      linear-algebra least-squares







      share|cite|improve this question















      I want to solve a least squares problem
      $$
      A x = b
      $$
      where $A$ is a $m times n$ lower trapezoidal matrix (zero above the diagonal), $x$ is $n times 1$, $b$ is $m times 1$, and $m > n$. So $A$ has the structure
      $$
      A = pmatrixL \ K
      $$
      where $L$ is $n times n$ lower triangular, and $K$ is $(m-n) times n$ and dense.



      I can't find a LAPACK or BLAS routine to call to solve this. Can this system be solved efficiently without needing to perform a QR or SVD on the matrix $A$? $A$ is already in $LQ$ form so I'm hoping this can be taken advantage of somehow.






      linear-algebra least-squares




      linear-algebra least-squares






      share|cite|improve this question















      share|cite|improve this question













      share|cite|improve this question




      share|cite|improve this question








      edited Aug 30 at 17:06

























      asked Aug 30 at 5:06









      vibe

      1438




      1438

























          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',
          convertImagesToLinks: true,
          noModals: false,
          showLowRepImageUploadWarning: true,
          reputationToPostImages: 10,
          bindNavPrevention: true,
          postfix: "",
          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%2f2899154%2ftrapezoidal-least-squares-system%23new-answer', 'question_page');

          );

          Post as a guest






















          active

          oldest

          votes













          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes















           

          draft saved


          draft discarded















































           


          draft saved


          draft discarded














          StackExchange.ready(
          function ()
          StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2899154%2ftrapezoidal-least-squares-system%23new-answer', 'question_page');

          );

          Post as a guest
































































          -

          這個網誌中的熱門文章

          How to combine Bézier curves to a surface?

          圖片
          Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier cur...
          閱讀完整內容

          Mutual Information Always Non-negative

          圖片
          Clash Royale CLAN TAG #URR8PPP up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 '12 at 15:38 Cameron Buie 83.6k 7 71 154 asked Jun 17 '12 at 15:30 Omri 359 3 13 3 Convexity of the function $tmapsto tlog t$. – Did Jun 17 '12 at 15:33 In addition, the convexity properties require the coefficients in the linear combination sum 1. Then, as p(x,y) is a probability distribution, it fullfits such condition. – Francisco Javier Delgado Ceped Aug 10 at 18:44 add a comment  |  up vote 10 down vote favorite 6 What is the simplest proof that mutual information is always non-negative? i.e., $I(X;Y)ge0$ probability-theory share | cite | improve this question edited Jun 17 ...
          閱讀完整內容

          Why am i infinitely getting the same tweet with the Twitter Search API?

          圖片
          up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia...
          閱讀完整內容