Abstract Singular value decomposition (SVD) beamforming is an attractive tool for reducing the energy consumption of data transmissions in wireless sensor networks whose nodes are equipped with multiple antennas. However, this method often not practical due to two important shortcomings: it requires channel state information at transmitter and computation SVD matrix generally too complex. To de...

This is the supplemental material for [5]. It contains a more detailed description of the closed form algorithm to compute inverse kinematics based on the Paden-Kahan subproblems. For an extended and more detailed version of [5] we refer the reader to [7]. 1. Paden-Kahan subproblems We are interested in solving the following problem: exp(θ1ω̂1) exp(θ2ω̂2) exp(θ3ω̂3) = Rj . (1) This problem can be ...

The joint bidiagonalization (JBD) method has been used to compute some extreme generalized singular values and vectors of a large regular matrix pair . We make numerical analysis the underlying JBD process establish relationships between it two mathematically equivalent Lanczos bidiagonalizations in finite precision. Based on results analysis, we investigate convergence approximate show that, u...

Many popular solution methods for large discrete ill-posed problems are based on Tikhonov regularization and compute a partial Lanczos bidiagonalization of the matrix. The computational effort required by these methods is not reduced significantly when the matrix of the discrete ill-posed problem, rather than being a general nonsymmetric matrix, is symmetric and possibly indefinite. This paper ...

Computing a small number of singular values is required in many practical applications and it is therefore desirable to have efficient and robust methods that can generate such truncated singular value decompositions. A new method based on the Lanczos bidiagonalization and the Krylov-Schur method is presented. It is shown how deflation strategies can be easily implemented in this method and pos...

We present a practical and efficient means to compute the singular value decomposition (svd) of a quaternion matrix A based on bidiagonalization of A to a real bidiagonal matrix B using quaternionic Householder transformations. Computation of the svd of B using an existing subroutine library such as lapack provides the singular values of A. The singular vectors of A are obtained trivially from ...

Recently Xu 13] proposed a new algorithm for computing a Jacobi matrix of order 2n with a given n n leading principal submatrix and with 2n prescribed eigenvalues that satisfy certain conditions. We compare this algorithm to a scheme proposed by Boley and Golub 2], and discuss a generalization that allows the conditions on the prescribed eigenvalues to be relaxed.