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UID:72@cds.iisc.ac.in
DTSTART;TZID=Asia/Kolkata:20240830T160000
DTEND;TZID=Asia/Kolkata:20240830T170000
DTSTAMP:20240809T094946Z
URL:https://cds.iisc.ac.in/events/seminar-cds-202-0400-august-the-circulan
 t-decomposition-of-a-matrix-and-fast-multiplication-of-large-matrices/
SUMMARY:{Seminar} @ CDS: #202: 04:00 August: "The circulant decomposition o
 f a matrix and fast multiplication of large matrices."
DESCRIPTION:Department of Computational and Data Sciences\nDepartment Semin
 ar\n\n\n\nSpeaker : Murugesan Venkatapathi\,Department of Computational &a
 mp\; Data Sciences.\nTitle : The circulant decomposition of a matrix and f
 ast multiplication of large matrices.\nDate &amp\; Time : August 30\, 2024
 \, 4:00 PM\nVenue : # 202\, CDS Class room\n\n\n\nABSTRACT\nThe well-known
  singular-value decomposition of a matrix\, and the eigenvalue decompositi
 on of a non-defective square matrix\, have become indispensable in enginee
 ring and sciences. Here\, the matrix is a weighted sum of rank-one matrice
 s with the corresponding singular-value or the eigenvalue as the weight. T
 ypically\, a decomposition is useful if a few significant components in th
 e sum contain most of the required information in the matrix.\n\nAnother d
 ecomposition of a n x n matrix was proposed here at the Institute\, where 
 the matrix is a sum of 'n' circulant matrices (with fixed periodic relaxat
 ions on the unit circle). This decomposition is orthogonal with respect to
  a certain inner product of matrices and allows a simple projection for th
 e circulant matrices. Alternately\, a more efficient evaluation of all cir
 culant components is also possible in O(n^2 . logn) operations exploiting 
 the Fast-Fourier-Transform (FFT). Note that a circulant matrix has at most
  'n' unique entries cyclically permuting both in its rows and columns. Rel
 atively few dominant circulant components may be sufficient in approximati
 ng a dense matrix when it has some periodicity in its entries. For such ma
 trices\, this decomposition was used in approximating eigenvalues and spar
 se similarity transformations\, and to precondition linear solvers.\n\nMor
 e generally\, the circulant decomposition was recently used to demonstrate
  iterative multiplication of two matrices in O(n^2 . logn^2) i.e. Õ(n^2) 
 arithmetic operations\, with well-bounded relative errors less than 1% unl
 ike other restricted methods approximating matrix multiplication. Further\
 , this decomposition may have additional gains in a quantum computation. T
 he talk is designed to introduce this matrix decomposition to students.\n\
 n\n\nALL ARE WELCOME
CATEGORIES:Events,Talks
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