An iteration method for the solution of the eigenvalue problem of linear differential and integral operators

Abstract

The p rese nt in vestigation designs a syste mat ic method for findin g the late nt I'oots and t he prin cipa l axes of a matrix, with ou t redu cin g t he o rd er of t he matri x. It is ch aracteri zed by a wide fi eld of appli ca b ili ty a nd great acc uracy, s ince t he a cc um ulat io n of ro undi ng errors is a vo id ed, t hrough t he p rocess of " minimi zed ite ratio ns". Mor eover, t he mcth od leads to a we ll co n ve rge nt s uccessiv e a pp rox im at io n p r occd ure by whi ch t he solu t io n of in tegr a l eq uatio ns of th e Fred holm t . v pe a nd t he so lu tion of t he eige n value prob lem of lin ear dilleren tia l a nd integ ra l o perators rn ay be acco m plished .

Using the Diphosphanyl Radical as a Potential Spin Label: Effect of Motion on the EPR Spectrum of an R1(R2)PPR1 Radical

“…The spectrum is finally calculated by the program TDLL, which processes the Lanczos tridiagonal matrix generated by EPRLL. [6,7] (The details are the same as those described in the SF procedure, to which reference should be made.) The simulations were carried out on a PC and visualized with the Microcal Origin 6.0 software.…”

Structure-Preserving Model Order Reduction of RCL Circuit Equations

“…The relation (35) can also be verified directly using the identity (27), (26), the definition of the matrix B in (23), and the definitions of the matrices M , D, K, and F in (15). …”

“…PVL [9,10] and its multi-port version MPVL [11] use variants of the Lanczos process [26] to stably compute reduced-order models that represent Padé or matrix-Padé approximations [5] of the circuit transfer function. SyPVL [21] and its multi-port version SyMPVL [12,23,24] are versions of PVL and MPVL, respectively, that are tailored to RCL circuits.…”

Implementation and use of a direct, partially integral‐driven non‐Dyson propagator method for molecular ionization

“…[20][21][22][23] As general subspace iteration approaches, they can in principle be used to obtain the full spectrum of a given large matrix, but in fact they have been designed and are tuned to obtain a subset of the whole eigenvalue spectrum. In the case of inner-valence ionization calculations, this useful subset rapidly becomes quite large, easily reaching hundreds if not thousands of solutions for moderately sized molecules.…”