| This paper demonstrates that, in general, implementations of circuit reduction methods can produce unstable and non-passive models even when such outcomes are theoretically proven to be impossible. The reason for this apparent contradiction is the numeric roundo inherent in any nite-precision computer implementation. This paper introduces a new variant of the symmetric, multiport, Pad e via L...

We present a method to approximate functionals Trf(A) of very high-dimensional hermitian matrices A represented as Matrix Product Operators (MPOs). Our method is based on a reformulation of a block Lanczos algorithm in tensor network format. We state main properties of the method and show how to adapt the basic Lanczos algorithm to the tensor network formalism to allow for high-dimensional comp...

Researchers use NFS (Number Field Sieve) method with Lanczos algorithm to analyze big-sized RSA keys. NFS method includes the integer factorization process and nullspace computation of huge sparse matrices. Parallel processing is indispensible since sequential computation requires weeks (even months) of CPU time with supercomputers even for 150-digit RSA keys. This paper presents details of imp...

We study the Lanczos method for solving symmetric linear systems with multiple right-hand sides. First, we propose a numerical method of implementing the Lanczos method, which can provide all approximations to the solution vectors of the remaining linear systems. We also seek possible application of this algorithm for solving the linear systems that occur in continuation problems. Sample numeri...

An \industrial strength" algorithm for solving sparse symmetric generalized eigenproblems is described. The algorithm has its foundations in known techniques in solving sparse symmetric eigenproblems, notably the spectral transformation of Ericsson and Ruhe and the block Lanczos algorithm. However, the combination of these two techniques is not trivial; there are many pitfalls awaiting the unwa...

We show constructively that, under certain regularity assumptions, any system of coupled linear differential equations with variable coefficients can be tridiagonalized by a time-dependent Lanczos-like method. The proof we present formally establishes the convergence so-called ?-Lanczos algorithm and yields full characterization algorithmic breakdowns. From there, solution original is available...

Article history: Received 18 May 2010 Received in revised form 5 July 2010 Accepted 7 July 2010 Available online 15 July 2010