A class of restarted randomized surrounding methods are presented to accelerate the algorithms by techniques for solving linear equations. Theoretical analysis shows that proposed method converges under row selection rule and convergence rate in expectation is also addressed. Numerical experiments further demonstrate efficient outperform existing overdetermined underdetermined equations, as wel...

An infestation of termites is weakening mathematical writing. We all too often resort to wishy-washy conditionals such as ‘can be’ or ‘wish to’ hidden within the body of sentences. Just as termites weaken a building, these conditionals erode writing by turning what should be definite statements into weak conditionals. Get rid of them. If in your analysis or computational experiments you do some...

This is a textbook about algorithms for computing with modular forms. It is nontraditional in that the primary focus is not on underlying theory; instead, it answers the question “how do you explicitly compute spaces of modular forms?”

The harmonic Arnoldi method can be used to compute some eigenpairs of a large matrix, and it is more suitable for finding interior eigenpairs. However, the harmonic Ritz vectors obtained by the method may converge erratically and may even fail to converge, so that resulting algorithms may not perform well. To improve convergence, a refined harmonic Arnoldi method is proposed that replaces the h...

This paper describes an alternative to modulo scheduling for loops, in which the first step is to divide instructions into stages by solving a series of min-cut problems constructed from the code graph of the unscheduled loop body. Our algorithm is formulated and implemented in terms of the code graphs of our own “declarative assembly language” for CELL SPUs. We have measured an average 20% red...

We present some properties of explicitly quasiconvex functions, which play an important role in both multicriteria and scalar optimization. Some of these results were recently obtained together with Ovidiu Bagdasar during a research visit at the University of Derby (UK), within the project