Matrix completion problems of block type

The solvability, either unconditional or under certain conditions, is proved for three matrix completion problems of block type. Being a problem of block type means that a matrixA must be constructed with a prescribed characteristic polynomial and one or several blocks in a 2 × 2 partition also prescribed. For the problems under analysis, one prescribes, respectively, (a) the blockA ₁₂; (b) the blockA ₁₁; (c) the blocksA ₁₁ andA ₁₂. We discuss our experience in implementing the algorithms that solve the problems above as procedures in the symbolic computation system MAPLE. Translated fromMatematicheskie Zametki, Vol. 67, No. 6, pp. 863–873, June, 2000. The first author was supported by the Russian Foundation for Basic Research under grant No. 97-01-00927.