LARGE SVD COMPUTATIONS FOR ANALYSIS OF INVERSE PROBLEMS IN GEOPHYSICS

This paper describes the implementation of a new algorithm to compute the Truncated Singular Value Decomposition (T-SVD) of matrices with fast decreasing singular values (such as Born approximation matrices). This method is based on a Low-rank approximations which extracts the most important information contained in the matrix. The largest singular values and their left and right singular vectors can then be approximated numerically without performing any operation using the full matrix. This property decreases significantly the memory usage and increases the performance (FLOPS) while getting the T-SVD. The low-rank approximation is computed thanks to the Cross Approximation (CA) technique. Validations tests demonstrate the accuracy of the method, both in terms of singular values and singular vectors. High performance of matrix-matrix operations on intermediate steps is archived by using BLAS and LAPACK components from Intel Math Kernel Library (Intel MKL) that is optimized for Intel architecture and parallelized via OpenMP. Performance tests showed more than ten times performance on one-thread system. Algorithm has large opportunity for parallelization both on shared memory systems (using OMP parallelization) and on distributed ones (MPI parallelization).