The present collection contains the results reported in 1970 at the Seminar on Approximate Com putations held by the Leningrad Section of the Mathematical Institute. Two trends are represented in the collection: automatic programming and numerical methods of analysis. V. N. Faddeeva CONTENTS On the Main Concepts of Parallel Sequencing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 T. A. Tushkina and K. V. Shakhbazyan The Solution of Certain Parallel Sequencing Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 T. A. Tushkina and K. V. Shakhbazyan Choice of Enumeration in Parallel Sequencing Problems. . . . . . . . . . . . . . . . . . . . . . . . . . 13 K. V. Shakhbaz yan The PRORAB-Computer III (P, v) M-20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 T. N. Smirnova, A. A. Aleksandrova, Yu. V. Rybakova, and N. A. Solov'eva Application of the PRORAB-Computer III (P, v) M-20 to the Solving of Linear Programming Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 T. N. Smirnova On a Matrix Inversion Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 V. D. Vulichevich The Solution of a Particular Eigenvalue Problem for Certain Matrices of Special Form. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 V. D. Vulichevich and V. N. Kublanovskaya Solution of a Particular Eigenvalue Problem for a Polynomial Matrix. . . . . . . . . . . . . . . . . 65 M. I. Mavlyanova On a Method for Constructing the Matrix Solution for a Polynomial Matrix. . . . . . . . . . . . . . . 71 M. I. Mavlyanova On One Approach to the Solution of the Inverse Eigenvalue Problem. . . . . . . . . . . .. . . . . . . 80 V. N. Kublanovskaya Convergence of the Method of Lines when Solving Nonlinear Parabolic Boundary Value Problems with Discontinuous Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 A. P. Kubanskaya Some Applications of the Five-Point Scheme of the Method of Lines . . . . . . . . . . . . . . . . . . 93 A. P. Kubanskaya On Expansions into Nonminimal Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 L. N.