Numerical analysis is the study of algorithms for the problems of continuous mathematics. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences & even the arts have adopted elements of scientific computations. Numerical linear algebra is essential to quantitative psychology, stochastic differential equations & Markov chains are essential in simulating living cells for medicine & biology. In recent years, a number of sophisticated methods for dealing with ordinary and partial differential equations, inverse & ill-posed problems, learning machines, have been developed in the applied mathematics community.The availability of these novel methods provides the possibility to address biological problems without precedent and with unmatched complexity, like genome-wide system analysis, structural & dynamic characterization of complex biological networks, high-throughput feature analysis. Due to the huge amount of data often involved in these applications, we make a significant effort to merge state-of-the-art techniques of numerical analysis with high performance computing, to produce tools able to manage large-scale problems within reasonable computer time.