We propose an algebraic method for the design of tabular parsing algorithms which uses parsing schemata [7]. The parsing strategy is expressed in a tree algebra. A parsing schema is derived from the tree algebra by means of algebraic operations such as homomorphic images, direct products, subalgebras and quotient algebras. The latter yields a tabular interpretation of the parsing strategy. The proposed method allows simpler and more elegant correctness proofs by using general theorems and is not limited to left-right parsing strategies, unlike current automaton-based approaches. Furthermore, it allows to derive parsing schemata for linear indexed grammars (LIG) from parsing schemata for context-free grammars by means of a correctness preserving algebraic transformation. A new bottom-up head corner parsing schema for LIG is constructed to demonstrate the method.