mloss.org Toeblitz Toolkit for Fast Toeplitz Matrix Operationshttp://mloss.orgUpdates and additions to Toeblitz Toolkit for Fast Toeplitz Matrix OperationsenWed, 13 Aug 2014 02:21:36 -0000Toeblitz Toolkit for Fast Toeplitz Matrix Operations 1.03http://mloss.org/software/view/496/<html><p>Toeplitz matrices arise naturally in machine learning whenever a stationary kernel is evaluated on equally spaced indices; one common example is the use of Gaussian processes to model time series data. Unfortunately, the usefulness of kernel methods involving Toeplitz matrices is limited by both the O(n^2) memory requirements and the O(n^3) runtime complexity of key matrix operations such as determinants and linear solves. </p> <p>Toeblitz is a MATLAB/Octave package for operations on positive definite Toeplitz matrices. It uses existing findings from linear algebra to perform the following for any positive definite Toeplitz matrix T: </p> <p>(i) solve Toeplitz systems Tx = b in O(n*log(n)) time and O(n) memory </p> <p>(ii) compute Toeplitz matrix inverses T^(-1) (with free log determinant) in O(n^2) time and memory </p> <p>(iii) compute Toeplitz log determinants (without inverses) in O(n^2) time and O(n) memory </p> <p>(iv) compute traces of products A*T for any matrix A and a Toeplitz matrix T, in minimal O(n^2) time and memory. </p></html>john cunningham, william zhangWed, 13 Aug 2014 02:21:36 -0000http://mloss.org/software/rss/comments/496http://mloss.org/software/view/496/kernelmatrix librarygaussian processtoeplitz