FORM matters: Fast symbolic computation under UNIX

Symbolic computation of the Duggal transform

Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...

Fast Matrix Multiplication and Symbolic Computation

The complexity of matrix multiplication (hereafter MM) has been intensively studied since 1969, when Strassen surprisingly decreased the exponent 3 in the cubic cost of the straightforward classical MM to log2(7) ≈ 2.8074. Applications to some fundamental problems of Linear Algebra and Computer Science have been immediately recognized, but the researchers in Computer Algebra keep discovering mo...

Fast Computation of a Complex Quadratic Form

with t t t j ε ε ε Im Re + = , where } {Re t ε and } {Im t ε are independent real Gaussian white noise processes each with zero mean and variance 2 2 σ . These processes have been widely used to model the noise component in data models consisting of a deterministic signal and an additive noise. The pure harmonic signal, the damped harmonic signal, and the polynomial phase signal can be given as...

Systems management under UNIX - and UNIX-like systems

Libckpt: Transparent Checkpointing under UNIX

Checkpointing is a simple technique for rollback recovery: the state of an executing program is periodically saved to a disk le from which it can be recovered after a failure. hile recent research has developed a collection of powerful techniques for minimizing the overhead of writing checkpoint les, checkpointing remains unavailable to most application developers. In this paper we describe lib...