TY - JOUR
T1 - Some Integral Equations with Nonsymmetric Separable Kernels
AU - ANDERSON, Brian D. O.
AU - KAILATH, T
PY - 1971
Y1 - 1971
N2 - It is shown that the eigenvalues and eigenfunctions for the class of “separable” or “semidegenerate” kernels can be determined from the solution of a linear differential equation, which is usually more amenable to machine solution. The theory is extended to solve a simultaneous diagonalization problem for two separable kernels. Finally, some new connections are obtained between Riccati differential equations and Fredholm integral equations of the second kind. The results specialize to previously known results for symmetric separable kernels.
AB - It is shown that the eigenvalues and eigenfunctions for the class of “separable” or “semidegenerate” kernels can be determined from the solution of a linear differential equation, which is usually more amenable to machine solution. The theory is extended to solve a simultaneous diagonalization problem for two separable kernels. Finally, some new connections are obtained between Riccati differential equations and Fredholm integral equations of the second kind. The results specialize to previously known results for symmetric separable kernels.
UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=anu_research_portal_plus2&SrcAuth=WosAPI&KeyUT=WOS:A1971J847600009&DestLinkType=FullRecord&DestApp=WOS_CPL
U2 - 10.1137/0120065
DO - 10.1137/0120065
M3 - Article
SN - 0036-1399
VL - 20
SP - 659
EP - 669
JO - SIAM Journal on Applied Mathematics
JF - SIAM Journal on Applied Mathematics
IS - 4
ER -