## Direct and iterative methods for the solution of linear operator equations in Hilbert space

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- Trans. Amer. Math. Soc.
**105**(1962), 136-175 Request permission

## References

- M. Altman,
*A simple practical method and a compact computing scheme for the solution of linear equations in Hilbert space*, Bull. Acad. Polon. Sci. Cl. III.**5**(1957), 29–33, IV (1 plate) (English, with Russian summary). MR**0085446** - Felix E. Browder,
*Functional analysis and partial differential equations. I*, Math. Ann.**138**(1959), 55–79. MR**107818**, DOI 10.1007/BF01369666
R. Courant and D. Hilbert, - Werner Greub and Werner Rheinboldt,
*On a generalization of an inequality of L. V. Kantorovich*, Proc. Amer. Math. Soc.**10**(1959), 407–415. MR**105028**, DOI 10.1090/S0002-9939-1959-0105028-3 - R. M. Hayes,
*Iterative methods of solving linear problems on Hilbert space*, Contributions to the solution of systems of linear equations and the determination of eigenvalues, National Bureau of Standards Applied Mathematics Series, No. 39, U.S. Government Printing Office, Washington, D.C., 1954, pp. 71–103. MR**0066563** - L. V. Kantorovič,
*Functional analysis and applied mathematics*, Uspehi Matem. Nauk (N.S.)**3**(1948), no. 6(28), 89–185 (Russian). MR**0027947** - L. V. Kantorovič,
*Approximate solution of functional equations*, Uspehi Mat. Nauk (N.S.)**11**(1956), no. 6(72), 99–116 (Russian). MR**0083696**
M. V. Keldysh, - A. D. Lyaško,
*The convergence of Galerkin type methods*, Dokl. Akad. Nauk SSSR**120**(1958), 242–244 (Russian). MR**0097882** - P. D. Lax and A. N. Milgram,
*Parabolic equations*, Contributions to the theory of partial differential equations, Annals of Mathematics Studies, no. 33, Princeton University Press, Princeton, N.J., 1954, pp. 167–190. MR**0067317** - A. E. Martynjuk,
*On a generalization of a variational method*, Dokl. Akad. Nauk SSSR (N.S.)**117**(1957), 374–377 (Russian). MR**0108725**
S. G. Mikhlin, - S. G. Mihlin,
*On Ritz’s method*, Dokl. Akad. Nauk SSSR (N.S.)**106**(1956), 391–394 (Russian). MR**0076314** - F. J. Murray,
*The solution of linear operator equations*, J. Math. Phys. Mass. Inst. Tech.**22**(1943), 148–157. MR**9091**, DOI 10.1002/sapm1943221148 - N. I. Pol′skiĭ,
*On the convergence of certain approximate methods of analysis*, Ukrain. Mat. Ž.**7**(1955), 56–70 (Russian). MR**0070978** - William T. Reid,
*Symmetrizable completely continuous linear transformations in Hilbert space*, Duke Math. J.**18**(1951), 41–56. MR**45314** - Frigyes Riesz and Béla Sz.-Nagy,
*Functional analysis*, Frederick Ungar Publishing Co., New York, 1955. Translated by Leo F. Boron. MR**0071727** - G. A. Ždanov,
*On the convergence of a modification of Galerkin’s method*, Dokl. Akad. Nauk SSSR (N.S.)**115**(1957), 223–225 (Russian). MR**0109954**

*Methoden der Mathematischen Physik*, 2nd Ed., Springer, Berlin, 1931. K. Friedrichs,

*Spektraltheorie halbbeschränkter Operatoren*, Math. Ann.

**109**(1934) 465-487, 685-713.

*On the method of Galerkin for the solution of boundary-value problems*, Izv. Akad. Nauk SSSR Ser. Mat.

**6**(1942), 307-330. M. A. Krasnoselsky and S. G. Krein,

*Iterative method with minimal residuals*, Mat. Sb.

**31**(

**73**) (1952), 315-334. M. Kravchuk,

*Application of the method of moments to the solution of linear differential and integral equations*, Ukrain. Akad. Nauk, Kiev (1932). N. M. Krilov,

*Les méthodes de solution approchée des problems de la physique mathématique*, Coll. Mem. de Math., No

**49**(1931), Paris.

*Direct methods in mathematical physics*, Moskva-Leningrad, 1950.

## Additional Information

- © Copyright 1962 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**105**(1962), 136-175 - MSC: Primary 65.35
- DOI: https://doi.org/10.1090/S0002-9947-1962-0145651-8
- MathSciNet review: 0145651