{"id":{"repo_id":"nps","oai_identifier":"oai:calhoun.nps.edu:10945/28596"},"canonical_url":"https://search.dev.ndltd.org/etd/nps/oai:calhoun.nps.edu:10945/28596","repository":{"repo_id":"nps","name":"Naval Postgraduate School","base_url":"https://calhoun.nps.edu/server/oai/request"},"display":{"title":"Tensor formulations for the modelling of discrete-time nonlinear and multidimensional systems.","abstract":"The modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order.","abstract_html":"The modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order.","abstract_has_math":false,"creators":["Lenk, Peter John"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Electrical and Computer Engineering","school":null,"contributors":[],"advisors":["Parker, Sydney R."],"committee_chairs":[],"committee_members":[],"year":1985,"date_issued":"1985-09","date_published":"1985-09","updated_at":"2026-07-27T20:25:42Z","subjects":[],"languages":["en_US"],"rights":["Copyright is reserved by the copyright owner"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/10945/28596","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Parker, Sydney R."]},{"key":"dc:contributor.department","label":"Department","values":["Electrical and Computer Engineering"]},{"key":"dc:creator","label":"Author","values":["Lenk, Peter John"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["September 1985"]},{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2013-02-15T23:34:16Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-02-15T23:34:16Z"]},{"key":"dc:date.issued","label":"Date","values":["1985-09"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_US"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright is reserved by the copyright owner"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/10945/28596"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order."]},{"key":"dc:title","label":"Title","values":["Tensor formulations for the modelling of discrete-time nonlinear and multidimensional systems."]}]}],"canonical_facts":{"dc:contributor.advisor":["Parker, Sydney R."],"dc:contributor.department":["Electrical and Computer Engineering"],"dc:creator":["Lenk, Peter John"],"dc:date":["September 1985"],"dc:date.accessioned":["2013-02-15T23:34:16Z"],"dc:date.available":["2013-02-15T23:34:16Z"],"dc:date.issued":["1985-09"],"dc:description.abstract":["The modelling of nonlinear and multidimensional systems from input and/or output measurements is considered. Tensor concepts are used to reformulate old results and develop several new ones. These results are verified through non-trivial computer simulations. A generalized tensor formulation for the modelling of discrete-time stationary nonlinear systems is presented. Tensor equivalents of the normal equations are derived and several efficient methods for their solution are discussed. Conditions are established that ensure a diagonal correlation tensor so that a solution can be obtained directly without matrix inversion. Using a tensor formulation, a new proof of the Generalized Lattice Theory is obtained. Tensor extensions of the Levinson and Schur algorithms are presented. New two-dimensional (2-D) lattice parameter models are derived. Using the tensor form of the Generalized Lattice Theory the 2-D multi-point error order-updates are decomposed into 0(N ) single point updates. 2-D extensions of the Levinson and Schur algorithms are given. The quarter plane lattice is considered in detail, first in a general form, then in forms which reduce the computational complexity by assuming shift-invariance. Based on the 2-D lattice, a new nonlinear lattice model is developed. The model is capable of updates in the nonlinear as well as time order."],"dc:identifier.uri":["https://hdl.handle.net/10945/28596"],"dc:language.iso":["en_US"],"dc:rights":["Copyright is reserved by the copyright owner"],"dc:title":["Tensor formulations for the modelling of discrete-time nonlinear and multidimensional systems."],"dc:type":["Thesis"]},"updated_at":"2026-07-27T20:25:42Z"}