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A novel technique based on the Full Orthogonalization Arnoldi (FOA) isproposed to perform Dynamic Mode Decomposition (DMD) for a sequence ofsnapshots. A modification to FOA is presented for situations where the matrix$A$ is unknown, but the set of vectors $\{A^{i-1}v_1\}_{i=1}^{N-1}$ are known.The modified FOA is the kernel for the proposed projected DMD algorithm termed,FOA based DMD. The proposed algorithm to compute DMD modes and eigenvalues i)does not require Singular Value Decomposition (SVD) for snapshot matrices $X$with $\kappa_2(X) \ll 1/\epsilon_m$, where $\kappa_2(X)$ is the 2-normcondition number of the snapshot matrix and $\epsilon_m$ is the relativeround-off error or machine epsilon, ii) has an optional rank truncation stepmotivated by round off error analysis for snapshot matrices $X$ with$\kappa_2(X) \approx 1/\epsilon_m$, iii) requires only one snapshot at a time,thus making it a 'streaming' method even with the optional rank truncationstep, iv) consumes less memory and requires less floating point operations toobtain the projected matrix than existing projected DMD methods and v) lendsitself to easy parallelism as the main computational kernel involves onlyvector additions, dot products and matrix vector products. The new technique istherefore well-suited for DMD of large datasets on parallel computingplatforms. We show both theoretically and using numerical examples that for FOAbased DMD without rank truncation, the finite precision error in the computedprojection of the linear mapping is $O(\epsilon_m\kappa_2(X))$. The proposedmethod is also compared to existing projected DMD methods for computationalcost, memory consumption and relative round off error. Error indicators arepresented that are useful to decide when to stop acquiring new snapshots. Theproposed method is applied to several examples of numerical simulations offluid flow.

A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data